Trigonometric Functions Case Study Questions Class 11 Maths Chapter 3

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Last Updated on July 22, 2025 by XAM CONTENT

Hello students, we are providing case study questions for class 11 Maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 11 Maths. In this article, you will find case study questions for cbse class 11 Maths chapter 3 Trigonometric Functions.

Chapter	Trigonometric Functions
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	11
Subject	Maths
Useful for	Class 11 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 11 Maths Chapterwise Case Study

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Table of Contents

Case Study Questions on Trigonometric Functions

Case Study Question 1

Case Study:
A mobile tower stands vertically on the ground and is observed from two points, A and B, on the same straight road at distances 100 meters and 200 meters from the base of the tower, respectively. The angle of elevation of the top of the tower from point A is \( 60^\circ \) and from point B is \( \theta \).

Questions:

Find the height of the tower, giving your answer in exact form (using surds if necessary).
Find the value of \( \theta \) (the angle of elevation from point B).
Explain the trigonometric principle used in determining the tower’s height from each observation point.

Solutions:

1. Height of the tower:

Let the height of the tower be \( h \). At point A, distance from the tower = 100 m, angle of elevation = \( 60^\circ \). \[ \tan 60^\circ = \frac{h}{100} \] \[ \sqrt{3} = \frac{h}{100} \] \[ h = 100\sqrt{3} \ \text{meters} \]

2. Value of angle \( \theta \) from point B (200m away):

\[ \tan \theta = \frac{h}{200} = \frac{100\sqrt{3}}{200} = \frac{\sqrt{3}}{2} \] \[ \tan \theta = \frac{\sqrt{3}}{2} \] Take \( \theta = \arctan\left(\frac{\sqrt{3}}{2}\right) \). So, \[ \boxed{\theta = \arctan\left(\frac{\sqrt{3}}{2}\right)} \approx 40.9^\circ \]

3. Explanation:
The principle used is the tangent of an angle in a right triangle: \( \tan \theta = \frac{\text{opposite side}}{\text{adjacent side}} \). Here, the height of the tower is the side opposite the angle of elevation, and the horizontal distance is the adjacent side. By setting up equations at each observation point, we relate height, distance, and angle using the tangent function.

Case Study Question 2

Case Study:
A flagpole stands on a hill. From a point P on horizontal ground, the angle of elevation to the bottom of the flagpole is \( 20^\circ \), and to the top of the flagpole (including the hill) is \( 40^\circ \). The point P is 80 meters away (measured horizontally) from the base of the hill.

Questions:

Find the height of the hill (\( h_1 \)), giving your answer in exact form (using surds if necessary).
If the height of the flagpole is \( h_2 \), find its value using the information provided.
Explain the trigonometric reasoning that relates the measured angles, heights, and distance in this scenario.

Solutions:

1. Height of the hill (\( h_1 \)):

Let \( h_1 \) be the height of the hill.
From point P, angle of elevation to bottom = \( 20^\circ \), distance = 80 m. \[ \tan 20^\circ = \frac{h_1}{80} \implies h_1 = 80 \tan 20^\circ \]

2. Height of flagpole (\( h_2 \)):

Let the total vertical height (hill + pole) = \( h_1 + h_2 \). From the same point, \[ \tan 40^\circ = \frac{h_1 + h_2}{80} \implies h_1 + h_2 = 80 \tan 40^\circ \] Subtracting \( h_1 \), we get: \[ h_2 = 80 (\tan 40^\circ – \tan 20^\circ) \]

3. Trigonometric reasoning:
This scenario applies the tangent of an angle in a right triangle: \( \tan \theta = \frac{\text{opposite}}{\text{adjacent}} \). The base of each right triangle formed has a length of 80 m, and the vertical sides correspond to the hill or (hill + pole). By using the two angles, we set up two equations and solve for both heights using the tangent function.

We hope the given case study questions for Trigonometric Functions Class 11 helps you in your learning.

Also check

Topics from which case study questions may be asked

Angles in different measures
Trigonometric ratios of standard angles
Signs of functions in quadrants
Trigonometric identities (Pythagorean)
Inverse trigonometric functions
Domain and range of trig functions

Key identities like sin²θ + cos²θ = 1 are foundational for solving equations and proving other trig relations.

Frequently Asked Questions (FAQs) on Trigonometric Functions Case Study Questions

Q1: What is a case study question in mathematics?

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should:
Read the problem carefully: Understand the scenario and identify the mathematical concepts involved.
Break down the problem: Divide the case study into smaller parts to manage the information better.
Apply relevant formulas and theorems: Use the appropriate mathematical tools to solve each part of the problem.

Q3: Why are case study questions included in the Class 11 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

Q4: Are there any online resources or tools available for practicing “Trigonometric Functions” case study questions?

A12: We provide case study questions for CBSE Class 11 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.