NCERT Solutions for Class 10 Maths Chapter 9: Some Applications of Trigonometry

Table of Contents

Introduction to Trigonometry Applications

In Class 10 Maths Chapter 9, we explore the real-world applications of trigonometry. This chapter focuses on solving problems related to heights and distances using trigonometric ratios. These concepts are widely used in fields like engineering, architecture, navigation, and physics.

Topics Covered in Chapter 9: Some Applications of Trigonometry

Introduction – Basic understanding of trigonometric concepts.
Heights and Distances – Applications of trigonometry to measure heights of objects and distances between points using angles of elevation and depression.
Summary – Key points and formulas covered in the chapter.

NCERT Solutions for Class 10 Maths Chapter 9 – All Exercises

This post provides NCERT solutions for all exercises of Chapter 9 – Some Applications of Trigonometry. These solutions are useful for board exam preparation, homework, and revision.

Example Problem from Chapter 9

Problem: A circus artist is climbing a 20-meter-long rope that is tightly stretched and tied from the top of a vertical pole to the ground. If the rope makes an angle of 30° with the ground, find the height of the pole.

Solution:
We use the sine formula: sin⁡(θ)=oppositehypotenuse\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}

Given:

Angle θ=30∘\theta = 30^\circ
Rope length (hypotenuse) = 20 m
Height of the pole (opposite side) = ?

sin⁡(30∘)=Height of Pole20\sin(30^\circ) = \frac{\text{Height of Pole}}{20}

Since sin⁡(30∘)=12\sin(30^\circ) = \frac{1}{2}, 12=Height of Pole20\frac{1}{2} = \frac{\text{Height of Pole}}{20} Height of Pole=20×12=10m\text{Height of Pole} = 20 \times \frac{1}{2} = 10 m

Final Answer: The height of the pole is 10 meters.