trigonometry case study questions class 10 with solutions

Class 10 Maths Case Study Questions Chapter 8 Introduction to Trigonometry

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Case study Questions in the Class 10 Mathematics Chapter 8  are very important to solve for your exam. Class 10 Maths Chapter 8 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 8  Introduction to Trigonometry

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In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Introduction to Trigonometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 8 Introduction to Trigonometry

Case Study/Passage-Based Questions

Question 1:

Answer: (d) 6m

(ii) Measure of ∠A =

Answer: (c) 45°

(iii) Measure of ∠C =

(iv) Find the value of sinA + cosC.

Answer: (d) 2√2

(v) Find the value of tan 2 C + tan 2  A.

Answer: (c) 2

Question 2:

Answer: (a) 30°

(ii) The measure of  ∠C is

Answer: (c) 60°

(iii) The length of AC is 

Answer: (d)6√3m

(iv) cos2A =

Answer: (b)1/2

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Introduction to Trigonometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Chapter 8 Class 10 Introduction to Trignometry

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The chapter is updated according to the new NCERT, for 2023-2024 Board Exams.

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Trigonometry means studying relationship between measures of triangle. Usually, we talk about right triangles when we study trigonometry,

In this chapter, we will study

• What is sin, cos, tan ( Sine, cosine, tangent) ... and how they are found in a triangle
• What is sec, cosec, cot, and how is it related to sin, cos, tan.
• (Sin, cos, tan, sec, cosec, cot are known as Trigonometric Ratios)
• Then, we study Trigonometric ratios of specific angles l ike 0°, 30°, 45°, 60°, 90° ; and do some questions
• We study the formulas of sin (90 - θ) , cos (90 - θ), tan (90 - θ)
• And then we study Trigonometric Identities, and how other identities are derived from sin 2 θ + cos 2 θ = 1

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CBSE Class 10 Maths Case Study Questions for Chapter 9 - Some Applications of Trigonometry (Published By CBSE)

Check case study questions for cbse class 10 maths chapter 9 - some applications of trigonometry. these questions are published by the cbse itself for class 10 students..

Case study based questions are new for class 10 students. Therefore, it is quite essential that students practice with more of such questions so that they do not have problem in solving them in their Maths board exam. We have provided here the case study questions for CBSE Class 10 Maths Chapter 9 - Some Applications of Trigonometry. All these questions have been published by the Central Board of Secondary Education (CBSE) for the class 10 students. Therefore, students must solve all the questions seriously so that they may score the desired marks in their Maths exam.

Check Case Study Questions for Class 10 Maths Chapter 9:

CASE STUDY 1:

A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919. The teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42 metres) in height.

1. What is the angle of elevation if they are standing at a distance of 42m away from the monument?

Answer: b) 45 o

2. They want to see the tower at an angle of 60 o . So, they want to know the distance where they should stand and hence find the distance.

Answer: a) 25.24 m

3. If the altitude of the Sun is at 60 o , then the height of the vertical tower that will cast a shadow of length 20 m is

a) 20√3 m

b) 20/ √3 m

c) 15/ √3 m

d) 15√3 m

Answer: a) 20√3 m

4. The ratio of the length of a rod and its shadow is 1:1. The angle of elevation of the Sun is

5. The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level is

a) corresponding angle

b) angle of elevation

c) angle of depression

d) complete angle

Answer: a) corresponding angle

CASE STUDY 2:

A Satellite flying at height h is watching the top of the two tallest mountains in Uttarakhand and Karnataka, them being Nanda Devi(height 7,816m) and Mullayanagiri (height 1,930 m). The angles of depression from the satellite, to the top of Nanda Devi and Mullayanagiri are 30° and 60° respectively. If the distance between the peaks of the two mountains is 1937 km, and the satellite is vertically above the midpoint of the distance between the two mountains.

1. The distance of the satellite from the top of Nanda Devi is

a) 1139.4 km

b) 577.52 km

d) 1025.36 km

Answer: a) 1139.4 km

2. The distance of the satellite from the top of Mullayanagiri is

Answer: c) 1937 km

3. The distance of the satellite from the ground is

Answer: b) 577.52 km

4. What is the angle of elevation if a man is standing at a distance of 7816m from Nanda Devi?

5.If a mile stone very far away from, makes 45 o to the top of Mullanyangiri mountain. So, find the distance of this mile stone from the mountain.

a) 1118.327 km

b) 566.976 km

Also Check:

Case Study Questions for All Chapters of CBSE Class 10 Maths

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Case Study and Passage Based Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry

• Last modified on: 10 months ago
• Reading Time: 3 Minutes

Case Study Questions:

Question 1:

Ananya is feeling so hungry and so thought to eat something. She looked into the fridge and found a bread pieces. She decided to make a sandwich. She cut the piece of bread diagonally and found it forms a right-angled triangle, with sides 4 cm, 4√3 cm and 8 cm.

On the basis of above information, answer the following questions.

(i) The value of ∠M is

D. None of these

(ii) The value of ∠K is

(iii) Find the value of tan M.

(iv) sec 2 M – 1 =

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You may also like:

Chapter 1 Real Numbers Chapter 2 Polynomials Chapter 3 Pair of Linear Equations in Two Variables C hapter 4 Quadratic Equations Chapter 5 Arithmetic Progressions Chapter 6 Triangles Chapter 7 Coordinate Geometry Chapter 8 Introduction to Trigonometry Chapter 9 Some Applications of Trigonometry Chapter 10 Circles Chapter 11 Constructions Chapter 12 Areas Related to Circles Chapter 13 Surface Areas and Volumes Chapter 14 Statistics Chapter 15 Probability

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CBSE Case Study Questions for Class 10 Maths Trigonometry Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Trigonometry  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 10 Maths Trigonometry PDF

Checkout our case study questions for other chapters.

• Chapter 6 Triangles Case Study Questions
• Chapter 7 Coordinate Geometry Case Study Questions
• Chapter 9 Some Applications of Trigonometry Case Study Questions
• Chapter 10 Circles Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

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• Case Study Class 10...

Case Study Class 10 Maths Questions

Table of Contents

myCBSEguide App

Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

• Real Numbers Case Study Question
• Polynomials Case Study Question
• Pair of Linear Equations in Two Variables Case Study Question
• Quadratic Equations Case Study Question
• Arithmetic Progressions Case Study Question
• Triangles Case Study Question
• Coordinate Geometry Case Study Question
• Introduction to Trigonometry Case Study Question
• Some Applications of Trigonometry Case Study Question
• Circles Case Study Question
• Area Related to Circles Case Study Question
• Surface Areas and Volumes Case Study Question
• Statistics Case Study Question
• Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

• Find the production in the 1 st year.
• Find the production in the 12 th year.
• Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

• Find the distance between Lucknow (L) to Bhuj(B).
• If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
• Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

• Find the distance PA.
• Find the distance PB
• Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

• What is the length of the line segment joining points B and F?
• The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
• What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

• If the first circular row has 30 seats, how many seats will be there in the 10th row?
• For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
• If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

• Draw a neat labelled figure to show the above situation diagrammatically.

• What is the speed of the plane in km/hr.

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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• Class 10 Maths

Important Questions Class 10 Maths Chapter 9 Applications of Trigonometry

Important questions for Class 10 Maths Chapter 9 Some Applications of Trigonometry are provided here for the board exams preparation. The questions are based on the new pattern of CBSE and are as per the revised syllabus. Students who are preparing CBSE 2022-2023 Maths exam are advised to practice these important questions of Some Applications of Trigonometry For Class 10 . Solving these questions will help students to score high marks in the questions asked from this chapter.

Trigonometry has more applications in our daily existence, and hence, the chapter is crucial for the board exam and valuable in many other fields. Most of the questions from this chapter are also asked in the competitive exams such as JEE etc.

• Applications of Trigonometry
• Trigonometry Formula For Class 10
• Trigonometry Table

Below, we have provided the questions of Chapter 9 Applications of Trigonometry with the solutions. Students can als o find additional qu estions without solutions for their practice.

Important Questions & Answers For Class 10 Maths Chapter 9 – Some Applications of Trigonometry

Q.1: The shadow of a tower standing on level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.

Let AB be the tower and BC be the length of its shadow when the sun’s altitude (angle of elevation from the top of the tower to the tip of the shadow) is 60° and DB be the length of the shadow when the angle of elevation is 30°.

Let us assume, AB = h m, BC = x m

DB = (40 +x) m

In the right triangle ABC,

tan 60° = AB/BC

h = √3 x……….(i)

In the right triangle ABD,

tan 30° = AB/BD

1/√3 =h/(x + 40) ……..(ii)

From (i) and (ii),

x(√3 )(√3 ) = x + 40

3x = x + 40

Substituting x = 20 in (i),

Hence, the height of the tower is 20√3 m.

Q. 2: A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Using given instructions, draw a figure. Let AC be the broken part of the tree. Angel C = 30 degrees.

To Find: Height of the tree, which is AB

From figure: Total height of the tree is the sum of AB and AC i.e. AB+AC

In right ΔABC,

Using Cosine and tangent angles,

cos 30° = BC/AC

We know that, cos 30° = √3/2

√3/2 = 8/AC

AC = 16/√3 …(1)

tan 30° = AB/BC

1/√3 = AB/8

AB = 8/√3 ….(2)

From (1) and (2),

Total height of the tree = AB + AC = 16/√3 + 8/√3 = 24/√3 = 8√3 m.

Q. 3: Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

Let AB and CD be the poles of equal height.

O is the point between them from where the height of elevation is taken. BD is the distance between the poles.

As per the above figure, AB = CD,

OB + OD = 80 m

In right ΔCDO,

tan 30° = CD/OD

1/√3 = CD/OD

CD = OD/√3 … (1)

In right ΔABO,

tan 60° = AB/OB

√3 = AB/(80-OD)

AB = √3(80-OD)

AB = CD (Given)

√3(80-OD) = OD/√3 (Using equation (1))

3(80-OD) = OD

240 – 3 OD = OD

Substituting the value of OD in equation (1)

CD = 20√3 m

⇒ OB = (80-60) m = 20 m

Therefore, the height of the poles are 20√3 m and the distance from the point of elevation are 20 m and 60 m respectively.

Q. 4:  An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

Let AB be the height of the observer and PR be the height of the tower.

Also, PB is the distance between the foot of the tower and the observer.

Consider θ as the angle of elevation of the top of the tower from the eye of the observer.

From the above figure,

AB = PQ = 1.5 m

PB = QA = 20 m

QR = PR – PQ = 22 – 1.5 = 20.5 m

In the right triangle AQR,

tan θ = QR/AQ

tan θ = 20.5/20.5 = 1

⇒ tan θ = tan 45°

Hence, the angle of elevation is 45°.

Q. 5: The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is √st.

Let BC = s; PC = t

Let the height of the tower be AB = h.

∠ABC = θ and ∠APC = 90° – θ

(∵ the angle of elevation of the top of the tower from two points P and B are complementary)

In triangle ABC,

tan θ = AC/BC = h/s ………..(i)

In triangle APC,

tan (90° – θ) = AC/PC = h/t

cot θ = h/t ………..(ii)

Multiplying (i) and (ii),

tan θ × cot θ = (h/s) × (h/t)

1 = h 2 /st

Hence, the height of the tower is √st.

Q.6: The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.

Let AB be the height of the tower.

The angle of elevation of the top of a tower from point P is 30°, i.e. ∠APB = 30°.

Given that, when the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°.

Thus, PQ = 20 m

Also, ∠AQB = 30° + 15° = 45°.

In right triangle ABQ,

tan 45° = AB/QB

h = x….(i)

In right triangle ABP,

tan 30° = AB/PB

1/√3 = h/(x + 20)

x + 20 = √3h  {from (i)}

h + 20 = √3h

√3h – h = 20

h = 20/(√3 – 1)

h = [20/(√3 – 1)] × [(√3 + 1)/(√3 + 1)]

= 20(√3 + 1)/(3 – 1)

= 20(√3 + 1)/2

= 10(√3 + 1)

Therefore, the height of the tower is 10(√3 + 1) m.

Q.7: A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.

Let AB be the vertical pole and AC be the length of the rope.

Also, the angle of elevation = ∠ACB = 30°

In right triangle ABC,

sin 30 = AB/AC

1/2 = AB/20

AB = 20/2 = 10

Therefore, the height of the vertical pole is 10 m.

Q.8: From the top of a 7 m high building, the angle of elevation of the top of a cable tower is

60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Let AB be the height of the building and CE be the height of the tower.

Also, A be the point from where the elevation of the tower is 60° and the angle of depression of its foot is 45°.

EC = DE + CD

From the figure,

CD = AB = 7 m

tan 45° = AB/BC

BC = 7 {since BC = AD}

Thus, AD = 7 m

In right triangle ADE,

tan 60° = DE/AD

⇒ DE = 7√3 m

EC = DE + CD = (7√3 + 7) = 7(√3 + 1)

Therefore, the height of the tower is 7(√3 + 1) m.

Video Lesson on Applications of Trigonometry

Practice Questions For Class 10 Maths Chapter 9 Some Applications of Trigonometry

• The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, what is the height of the hill? [Answer: 150 m]
• A bridge across the river makes an angle of 45° with the river bank. If the length of the bridge across the river is 150 m, what is the width of the river? [Answer: 75√2 m]
• There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are the points directly opposite to each other on the two banks, and in a line with the tree. If the angles of elevation of the top of the tree from P and Q are 30° and 45° respectively, find the height of the tree. [Answer: 36.6.m]
• From a point 20m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower. [Answer: 11.56 m]
• A flagstaff stands at the top of a 5m high tower. From a point on the ground, the angle of elevation of the top of the flagstaff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flagstaff. [Answer: 3.65 m]
• A tower subtends an angle α at a point A in the place of its base and the angle of depression of the foot of the tower at a point b ft. just above A is β. Prove that the height of the tower is b tan α cot β.
• A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 45°. Find the height of the tower. [Answer: 9.55m]
• The angle of elevation of a cloud from a point h metres above the surface of a lake is θ and the angle of depression of its reflection in the lake is φ. Prove that the height of the cloud above the lake is h[(tan φ + tan θ)/ (tan φ – tan θ)].
• The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings. [Answer: 4(3 + √3) m]
• A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower at a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point. [Answer: 3 sec]

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10th Class Mathematics Introduction to Trigonometry Question Bank

Done case based (mcqs) - introduction to trigonometry total questions - 35.

A) \[8\, cm\] done clear

B) \[\sqrt{65}\,cm\] done clear

C) \[7.5\,cm\] done clear

D) \[\sqrt{69}\,cm\] done clear

question_answer 2) The value of \[\tan x{}^\circ \] is:

A) \[\frac{7.5}{13}\] done clear

B) \[\frac{5}{4}\] done clear

C) \[\frac{4}{5}\] done clear

D) \[\frac{13}{7.5}\] done clear

question_answer 3) The value of \[\sec x{}^\circ \] is:

A) \[\frac{\sqrt{91}}{6}\] done clear

B) \[\frac{\sqrt{71}}{6}\] done clear

C) \[\frac{\sqrt{41}}{4}\] done clear

D) \[\frac{\sqrt{31}}{5}\] done clear

question_answer 4) The value of \[\sin y{}^\circ \] is:

A) \[\frac{4}{\sqrt{65}}\] done clear

B) \[\frac{4}{7}\] done clear

C) \[\frac{7}{4}\] done clear

D) \[\frac{\sqrt{65}}{7}\] done clear

question_answer 5) The value of \[\cot y{}^\circ \] is:

A) \[\frac{7}{4}\] done clear

C) \[\frac{\sqrt{65}}{4}\] done clear

A) \[\frac{\sqrt{34}}{5}\] done clear

B) \[\frac{\sqrt{34}}{3}\] done clear

C) \[\frac{5}{3}\] done clear

D) \[\frac{3}{\sqrt{34}}\] done clear

question_answer 7) The value of cosec R is:

A) \[\frac{\sqrt{29}}{5}\] done clear

B) \[\frac{\sqrt{29}}{2}\] done clear

C) \[\frac{2}{5}\] done clear

D) \[\frac{5}{\sqrt{29}}\] done clear

question_answer 8) The value of \[\tan S+\cot R\] is:

A) \[\frac{9}{4}\] done clear

B) \[\frac{5}{3}\] done clear

D) \[\frac{31}{15}\] done clear

question_answer 9) Value of \[{{\sin }^{2}}R-{{\cos }^{2}}S\] is:

A) \[0\] done clear

B) \[1\] done clear

C) \[\frac{97}{85}\] done clear

D) \[\frac{589}{986}\] done clear

question_answer 10) Value of \[{{\sin }^{2}}S-{{\cos }^{2}}R\] is:

A) \[30{}^\circ \] done clear

B) \[45{}^\circ \] done clear

C) \[60{}^\circ \] done clear

D) None of these done clear

question_answer 12) The measure of \[\angle C\] is:

question_answer 13) The length of AC is:

A) \[2\sqrt{3}\,m\] done clear

B) \[\sqrt{3}\,m\] done clear

C) \[4\sqrt{3}\,m\] done clear

D) \[6\sqrt{3}\,m\] done clear

question_answer 14) \[\cos 2A=\]

B) \[\frac{1}{2}\] done clear

C) \[\frac{1}{\sqrt{2}}\] done clear

D) \[\frac{\sqrt{3}}{2}\] done clear

question_answer 15) \[\sin \left( \frac{C}{2} \right)=\]

B) \[60{}^\circ \] done clear

C) \[45{}^\circ \] done clear

question_answer 17) The value of \[\angle K=\]

A) \[45{}^\circ \] done clear

B) \[30{}^\circ \] done clear

question_answer 18) Find the value of sec M.

A) \[\sqrt{3}\] done clear

B) \[\frac{2}{\sqrt{3}}\] done clear

C) \[1\] done clear

question_answer 19) \[{{\sec }^{2}}M-1=\]

A) \[\tan M\] done clear

B) \[\tan 2M\] done clear

C) \[{{\tan }^{2}}M\] done clear

question_answer 20) The value of \[\frac{{{\tan }^{2}}45{}^\circ -1}{{{\tan }^{2}}45{}^\circ +1}\]is:

C) \[2\] done clear

D) \[-1\] done clear

A) \[2m\] done clear

B) \[3m\] done clear

C) \[4m\] done clear

D) \[6m\] done clear

question_answer 22) Measure of \[\angle A=\]

question_answer 23) Measure of \[\angle C=\]

question_answer 24)   Find the value of \[\sin A+\cos C.\]

D) \[\sqrt{2}\] done clear

question_answer 25) Find the value of \[{{\tan }^{2}}C+{{\tan }^{2}}A\].

D) \[\frac{1}{2}\] done clear

A) \[5\,ft\] done clear

B) \[6\,ft\] done clear

C) \[8\,ft\] done clear

D) \[\frac{8}{\sqrt{3}}\,ft\] done clear

question_answer 27) In above triangle, what is the length of BC?

D) \[4\sqrt{3}\,ft\] done clear

question_answer 28) If \[\text{sin A}=\text{sin C},\]what will be the length of BC?

A) \[2ft\] done clear

B) \[4ft\] done clear

C) \[8ft\] done clear

D) \[4\sqrt{2}ft\] done clear

question_answer 29) If \[\sin (A+B)=\frac{1}{\sqrt{2}}\]and \[\cos (A-B)=\frac{\sqrt{3}}{2},\] \[0{}^\circ <A+B\le 90{}^\circ ,\] \[A>B\]then \[\angle A\]is:

B) \[37.5{}^\circ \] done clear

C) \[32.5{}^\circ \] done clear

D) \[35{}^\circ \] done clear

question_answer 30) If the length of AB doubles what will happen to the Length of AC?

A) remains same done clear

B) doubles the original lengthy done clear

C) become three times the original length done clear

D) become half of the original length done clear

A) \[\frac{8}{15}\] done clear

B) \[\frac{8}{17}\] done clear

C) \[\frac{15}{8}\] done clear

D) \[\frac{15}{17}\] done clear

question_answer 32) The value of \[\text{cosec}\,\,\text{P}\] is:

A) \[\frac{8}{17}\] done clear

B) \[\frac{15}{17}\] done clear

C) \[\frac{17}{8}\] done clear

D) \[\frac{17}{15}\] done clear

question_answer 33) The value of \[\frac{\sin R-\cos P}{\sin R+\cos P}\] is:

A) \[\frac{17}{30}\] done clear

B) \[\frac{30}{17}\] done clear

C) \[0\] done clear

D) \[1\] done clear

question_answer 34) The value of cot P is:

A) \[\frac{15}{17}\] done clear

B) \[\frac{17}{15}\] done clear

C) \[\frac{8}{15}\] done clear

D) \[\frac{15}{8}\] done clear

question_answer 35) The value of \[\tan R+\frac{3}{\sec P}-1\]is:

A) \[\frac{253}{136}\] done clear

B) \[\frac{357}{136}\] done clear

C) \[\frac{479}{136}\] done clear

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Case Based (MCQs) - Introduction to Trigonometry

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Case Study on Some Applications of Trigonometry Class 10 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Some Applications of Trigonometry Class 10 Maths can use this page to download the PDF file. 

The case study questions on Some Applications of Trigonometry are based on the CBSE Class 10 Maths Syllabus, and therefore, referring to the Some Applications of Trigonometry case study questions enable students to gain the appropriate knowledge and prepare better for the Class 10 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Some Applications of Trigonometry Class 10 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Some Applications of Trigonometry, therefore, they prepared a set of solutions along with the case study questions on Some Applications of Trigonometry.

The case study on Some Applications of Trigonometry Class 10 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Some Applications of Trigonometry case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Some Applications of Trigonometry Case Study Questions on Class 10 Maths?

There are three major reasons why one should solve Some Applications of Trigonometry case study questions on Class 10 Maths - all those major reasons are discussed below:

• To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 10 Maths students, therefore, it is important to solve Some Applications of Trigonometry Case study questions as it will help better prepare for the Class 10 board exam preparation.
• Develop Problem-Solving Skills: Class 10 Maths Some Applications of Trigonometry case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 10 students develop their problem-solving skills, which are essential for success in any profession rather than Class 10 board exam preparation.
• Understand Real-Life Applications: Several Some Applications of Trigonometry Class 10 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Some Applications of Trigonometry as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Some Applications of Trigonometry?

Students can choose their own way to answer Case Study on Some Applications of Trigonometry Class 10 Maths, however, we believe following these three steps would help a lot in answering Class 10 Maths Some Applications of Trigonometry Case Study questions.

• Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
• Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Some Applications of Trigonometry questions quickly.
• Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Some Applications of Trigonometry Class 10 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 10 Some Applications of Trigonometry?

 A few essential things to know to solve Case Study Questions on Class 10 Some Applications of Trigonometry are -

• Basic Formulas of Some Applications of Trigonometry: One of the most important things to know to solve Case Study Questions on Class 10 Some Applications of Trigonometry is to learn about the basic formulas or revise them before solving the case-based questions on Some Applications of Trigonometry.
• To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 10 Maths Some Applications of Trigonometry case study questions.
• Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

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CBSE Class 10 Maths Case Study Questions PDF

Download Case Study Questions for Class 10 Mathematics to prepare for the upcoming CBSE Class 10 Final Exam. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 10 so that they can score 100% on Boards.

CBSE Class 10 Mathematics Exam 2024  will have a set of questions based on case studies in the form of MCQs. The CBSE Class 10 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

Table of Contents

Chapterwise Case Study Questions for Class 10 Mathematics

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

The above  Case studies for Class 10 Maths will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

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Class 10 Maths Syllabus 2024

Chapter-1  real numbers.

Starting with an introduction to real numbers, properties of real numbers, Euclid’s division lemma, fundamentals of arithmetic, Euclid’s division algorithm, revisiting irrational numbers, revisiting rational numbers and their decimal expansions followed by a bunch of problems for a thorough and better understanding.

Chapter-2  Polynomials

This chapter is quite important and marks securing topics in the syllabus. As this chapter is repeated almost every year, students find this a very easy and simple subject to understand. Topics like the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of a polynomial, division algorithm for polynomials followed with exercises and solved examples for thorough understanding.

Chapter-3  Pair of Linear Equations in Two Variables

This chapter is very intriguing and the topics covered here are explained very clearly and perfectly using examples and exercises for each topic. Starting with the introduction, pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solving a pair of linear equations, substitution method, elimination method, cross-multiplication method, equations reducible to a pair of linear equations in two variables, etc are a few topics that are discussed in this chapter.

Chapter-4  Quadratic Equations

The Quadratic Equations chapter is a very important and high priority subject in terms of examination, and securing as well as the problems are very simple and easy. Problems like finding the value of X from a given equation, comparing and solving two equations to find X, Y values, proving the given equation is quadratic or not by knowing the highest power, from the given statement deriving the required quadratic equation, etc are few topics covered in this chapter and also an ample set of problems are provided for better practice purposes.

Chapter-5  Arithmetic Progressions

This chapter is another interesting and simpler topic where the problems here are mostly based on a single formula and the rest are derivations of the original one. Beginning with a basic brief introduction, definitions of arithmetic progressions, nth term of an AP, the sum of first n terms of an AP are a few important and priority topics covered under this chapter. Apart from that, there are many problems and exercises followed with each topic for good understanding.

Chapter-6  Triangles

This chapter Triangle is an interesting and easy chapter and students often like this very much and a securing unit as well. Here beginning with the introduction to triangles followed by other topics like similar figures, the similarity of triangles, criteria for similarity of triangles, areas of similar triangles, Pythagoras theorem, along with a page summary for revision purposes are discussed in this chapter with examples and exercises for practice purposes.

Chapter-7  Coordinate Geometry

Here starting with a general introduction, distance formula, section formula, area of the triangle are a few topics covered in this chapter followed with examples and exercises for better and thorough practice purposes.

Chapter-8  Introduction to Trigonometry

As trigonometry is a very important and vast subject, this topic is divided into two parts where one chapter is Introduction to Trigonometry and another part is Applications of Trigonometry. This Introduction to Trigonometry chapter is started with a general introduction, trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles, trigonometric identities, etc are a few important topics covered in this chapter.

Chapter-9  Applications of Trigonometry

This chapter is the continuation of the previous chapter, where the various modeled applications are discussed here with examples and exercises for better understanding. Topics like heights and distances are covered here and at the end, a summary is provided with all the important and frequently used formulas used in this chapter for solving the problems.

Chapter-10  Circle

Beginning with the introduction to circles, tangent to a circle, several tangents from a point on a circle are some of the important topics covered in this chapter. This chapter being practical, there are an ample number of problems and solved examples for better understanding and practice purposes.

Chapter-11  Constructions

This chapter has more practical problems than theory-based definitions. Beginning with a general introduction to constructions, tools used, etc, the topics like division of a line segment, construction of tangents to a circle, and followed with few solved examples that help in solving the exercises provided after each topic.

Chapter-12  Areas related to Circles

This chapter problem is exclusively formula based wherein topics like perimeter and area of a circle- A Review, areas of sector and segment of a circle, areas of combinations of plane figures, and a page summary is provided just as a revision of the topics and formulas covered in the entire chapter and also there are many exercises and solved examples for practice purposes.

Chapter-13  Surface Areas and Volumes

Starting with the introduction, the surface area of a combination of solids, the volume of a combination of solids, conversion of solid from one shape to another, frustum of a cone, etc are to name a few topics explained in detail provided with a set of examples for a better comprehension of the concepts.

Chapter-14  Statistics

In this chapter starting with an introduction, topics like mean of grouped data, mode of grouped data, a median of grouped, graphical representation of cumulative frequency distribution are explained in detail with exercises for practice purposes. This chapter being a simple and easy subject, securing the marks is not difficult for students.

Chapter-15  Probability

Probability is another simple and important chapter in examination point of view and as seeking knowledge purposes as well. Beginning with an introduction to probability, an important topic called A theoretical approach is explained here. Since this chapter is one of the smallest in the syllabus and problems are also quite easy, students often like this chapter

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NCERT Solutions for Class 10 Maths Chapter 8 Introduction To Trigonometry

NCERT Solutions Class 10 Maths Chapter 8 Introduction To Trigonometry are provided here to help the students of CBSE class 10. Our expert teachers prepared all these solutions as per the latest CBSE syllabus and guidelines. CBSE Class 10 Maths solutions provide a detailed and step-wise explanation of each answer to the questions given in the exercises of NCERT books.

CBSE Class 10 Maths Chapter 8 Introduction To Trigonometry Solutions

Below we have given the answers to all the questions present in Introduction To Trigonometry in our NCERT Solutions for Class 10 Maths chapter 8. In this lesson, students are introduced to a lot of important concepts that will be useful for those who wish to pursue mathematics as a subject in their future classes. Based on these solutions, students can prepare for their upcoming Board Exams. These solutions are helpful as the syllabus covered here follows NCERT guidelines.

NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.1

NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.2

NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.3

NCERT Solutions for Class 10 Maths Chapter 8 Exercise 8.4

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CBSE 10th Standard Maths Subject Some Applications of Trigonometry Case Study Questions 2021

By QB365 on 22 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) Measure of \(\angle\) ACB is equal to

(iii) Width of the river is 

(iv) Height of the other temple is

(v) Angle of depression is always

(ii) Value of DF is equal to

(iii) Value of h is

(iv) Height of the balloon from the ground is

(v) If the balloon is moving towards the building, then both angle of elevation will

(ii) If the angle made by the rope to the ground level is 45°, then find the distance between artist and pole at ground level.

(iii) Find the height of the pole if the angle made by the rope to the ground level is 30°.

(iv) If the angle made by the rope to the ground level is 30° and 3 m rope is broken, then find the height of the pole

(v) Which mathematical concept is used here?

(ii) If fireman place the ladder 5 m away from the wall and angle of elevation is observed to be 30°, then length of the ladder is

(iii) If fireman places the ladder 2.5 m away from the wall and angle of elevation is observed to be 60°, then find the height of the window. (Take \(\sqrt{3}\) = 1.73)

(iv) If the height of the window is 8 m above the ground and angle of elevation is observed to be 45°, then horizontal distance between the foot of ladder and wall is

(v) If the fireman gets a 9 m long ladder and window is at 6 m height, then how far should the ladder be placed?

(ii) Distance between two positions of the car is

(iii) Total time taken by the car to reach the foot of the building from starting point is

(iv) The distance of the observer from the car when it makes an angle of 60° is

(v) The angle of elevation increases

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Cbse 10th standard maths subject some applications of trigonometry case study questions 2021 answer keys.

(i) (b): The person who makes small angle of elevation is more closer to the balloon. \(\therefore\) Radlra is more closer to the balloon. (ii) (b):  \(\text { In } \Delta E F D, \tan 30^{\circ}=\frac{E D}{D F}\) \(\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{h}{D F} \) \(\Rightarrow \quad D F=h \sqrt{3} \mathrm{~m}\) (iii) (a): In \(\Delta\) GCE, \(\begin{array}{l} \tan 60^{\circ}=\frac{E C}{G C}=\frac{h+4}{D F} \\ \Rightarrow \quad \sqrt{3}=\frac{h+4}{\sqrt{3} h} \Rightarrow 3 h=h+4 \Rightarrow h=2 \end{array}\) (iv) (c): Height of the balloon from the ground = BE = BC + CD + DE = 2 + 4 + 2 = 8 m (v) (b)

(i) (c):   \(\text { In } \Delta A B C, \frac{A B}{B C}=\tan 60^{\circ}\) \(\Rightarrow \quad A B=25 \times \sqrt{3}\) \(\therefore\) Height of building is 25 \(\sqrt{3}\) m . (ii) (b):   \(\text { In } \Delta A B D, \frac{A B}{B D}=\tan 30^{\circ}\) \(\Rightarrow \frac{25 \sqrt{3}}{B D}=\frac{1}{\sqrt{3}} \Rightarrow B D=75 \mathrm{~m}\) \(\therefore\)  Distance between two positions of car = (75 - 25) m = 50m. (iii) (d): Time taken to cover 50 m distance = 6 sec. \(\therefore\) Time taken to cover 25 m distance = 3 sec. \(\therefore\) Total time taken by car = 6 sec + 3 sec = 9 sec (iv) (c):  \(\text { In } \Delta A B C, \frac{B C}{A C}=\cos 60^{\circ}\) \(\Rightarrow \quad \frac{25}{A C}=\frac{1}{2} \) \(\Rightarrow A C=50 \mathrm{~m}\) (v) (a)

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