NCERT Solutions For Class 10 Maths Chapter 9 Some Applications Of Trigonometry

Class 10 Maths Chapter 9 Trigonometry Overview

ToppersSky presents complete NCERT Solutions which are easy to understand for Class 10 Maths Chapter 9 which covers Some Applications of Trigonometry. The NCERT textbook questions are solved through a step-by-step process which includes detailed explanations that help students grasp every concept. Class 10 students can learn trigonometry through educational videos which use both 2D and 3D animations to teach the subject.

The solutions provide study materials which follow the most recent NCERT syllabus because they assist students in preparing for board exams with confidence. The answers are constructed in an organized format which helps students acquire proper exam answer writing skills. ToppersSky offers chapter notes, mind maps, important questions, practice sets, and podcasts as additional study materials which help students complete their revision work.

ToppersSky provides animated explanations together with organized study materials which enable students to develop strong trigonometry concepts while improving their performance in Class 10 Maths.

Download a PDF of the NCERT solutions for class 10 maths, chapter 9 on Some Applications Of Trigonometry.

ToppersSky provides complete chapter solutions for every NCERT Class 10 Maths chapter through structured solutions which detail every aspect of the chapters. The solutions enable students to resolve their uncertainties while they create a solid understanding of all concepts. The animation-based explanations together with the step-by-step answers enable students to understand each topic without experiencing any confusion.

Through ToppersSky’s NCERT Solutions for Class 10, students achieve complete confidence to solve complex problems which appear in all exercises. The animated video content together with comprehensive notes and practice sets provides students with improved understanding of concepts while they prepare for exams.

Class 10 board exam of mathematics, an important chapter for the students is “Some Applications of Trigonometry”. Usually, a considerable number of marks are given from this chapter. The question paper is divided into different sections carrying 1, 2, 3, and 4 marks. Students can also expect both short and long answer questions from this chapter and thus, a clear understanding is essential for scoring high.

ToppersSky offers full NCERT Solutions for Class 10 Maths Chapter 9 with detailed explanations. Not only through well organized solutions but also through Animation learning, students get a brilliant view of each problem’s solution method and how to write the answers properly in the exams.

Topics Covered in Chapter 9 – Some Applications of Trigonometry

Introduction

Students will learn how trigonometry is utilized in the real world. In previous chapters the trigonometric ratios were discussed. The students now know the role these ratios play in the solution of practical issues related to distances and heights. Trigonometry is among the oldest mathematical branches and was originally employed in the field of astronomy. With the aid of animated explanations in the app topperssky students are able to comprehend the way these concepts function in everyday scenarios.

Distances and Heights

This section provides important terms like line of sight angle of elevation and the angle of depression. They are utilized to determine the distance and height of objects without measuring them. Every numerical problem is solved with trigonometric ratios through an easy step-by-step approach. ToppersSky App offers video tutorials with animation, notes and practice tests to help make these concepts simple and understandable for students who are preparing for their exams.

Summary

The summary section aids students review all the crucial formulas and important aspects that are covered throughout the chapters. Revision in a short time using brain maps and notes that are structured aids students in remembering concepts for longer. This method of revision is beneficial not just to help with Maths as well, but for other subjects such as science class 10 as well as class 10 Social Science in which clarity of concepts is also crucial.

Why This Chapter Is Important

Students learn about the practical applications of trigonometry when they study this chapter which shows how trigonometry helps determine building and mountain heights and distance measurements that do not require direct measurement. In earlier times, astronomers used trigonometry to calculate the distance between the earth and stars. The system enables today’s users to determine their geographic location through the measurement of latitude and longitude. The educational process becomes more appealing and useful when students comprehend how these applications function.

Key Features of ToppersSky NCERT Solutions for Chapter 9

• The design is simple and easy to understand explanations
• Chapter-wise structured solutions
• Step-by-step approach to problem-solving
• Videos with animations for greater understanding
• Mind maps and notes to be taken for rapid revision
• Practice sets can help improve confidence
• Instructions on how to write answers to exams

ToppersSky helps students prepare with well-organized learning materials so they can improve their understanding in Maths and excel on exams. With animated learning apps and structured revision apps students are able to grasp complex trigonometry concepts with ease and increase their academic performance overall.

NCERT Questions and Answers of Class 10 Maths Chapter 9

Q.1 A circus artist climbs a rope that is 20 m long. The rope makes an angle of 30° with the ground. Find the height of the pole.

Solution:

Given:
AC = 20 m
Angle = 30°

Using sine formula:

sin 30° = AB / AC
1/2 = AB / 20

AB = 10 m

Therefore, the height of the pole is 10 m.

Q.2 The tree breaks during a storm and the top touches the ground making an angle of 30° with the ground. The distance from the base to the touching point is 8 m. Find the height of the tree.

Solution:

BC = 8 m

Using cosine:

cos 30° = BC / AC
√3/2 = 8 / AC

AC = 16 / √3

Using tangent:

tan 30° = AB / BC
1/√3 = AB / 8

AB = 8 / √3

Total height = AB + AC
= 8/√3 + 16/√3
= 24/√3
= 8√3 m

So, the height of the tree is 8√3 m.

Q.3 Two slides are planned. One is 1.5 m high and inclined at 30°. The other is 3 m high and inclined at 60°. Find the length of both slides.

Solution:

For 30° slide:

sin 30° = 1.5 / AC
1/2 = 1.5 / AC

AC = 3 m

For 60° slide:

sin 60° = 3 / PR
√3/2 = 3 / PR

PR = 2√3 m

So, the lengths are 3 m and 2√3 m.

Q.4 The angle of elevation of the top of a tower from a point 30 m away is 30°. Find the height of the tower.

Solution:

tan 30° = AB / 30
1/√3 = AB / 30

AB = 10√3 m

Therefore, the height of the tower is 10√3 m.

Q.5 A kite is flying at a height of 60 m. The string makes an angle of 60° with the ground. Find the length of the string.

Solution:

sin 60° = 60 / AC
√3/2 = 60 / AC

AC = 40√3 m

So, the string length is 40√3 m.

Q.6 A 1.5 m tall boy sees the top of a 30 m building. The angle of elevation changes from 30° to 60° as he walks closer. Find the distance he walked.

Solution:

Height from eye level = 30 − 1.5 = 28.5 m

Using tan 30°:

1/√3 = 28.5 / BD
BD = 28.5√3

Using tan 60°:

√3 = 28.5 / BC
BC = 28.5√3 / 3

Distance walked = BD − BC
= 19√3 m

So, the boy walked 19√3 m.

Q.7 From a point, the angles of elevation of a 20 m building and the top of a tower above it are 45° and 60°. Find the height of the tower.

Solution:

tan 45° = 20 / CD
CD = 20

tan 60° = AC / 20
AC = 20√3

Height of tower = AC − 20
= 20(√3 − 1) m

So, the height of the tower is 20(√3 − 1) m.

Q.8 A statue 1.6 m tall stands on a pedestal. From a point on the ground, the angles of elevation of the top of the statue and pedestal are 60° and 45°. Find the height of the pedestal.

Solution:

Using tan 45°:

BC = CD

Using tan 60°:

√3CD = 1.6 + BC

BC(√3 − 1) = 1.6

BC = 0.8(√3 + 1) m

So, the height of the pedestal is 0.8(√3 + 1) m.

Q.9 The angle of elevation of the top of a building from a tower base is 30°, and the angle of elevation of the top of the tower from the building base is 60°. The tower height is 50 m. Find the height of the building.

Solution:

tan 60° = 50 / BC
BC = 50 / √3

tan 30° = AB / BC
AB = 50 / 3 m

So, the height of the building is 50/3 m.

Q.10 Two poles of equal height stand opposite each other across an 80 m wide road. From a point between them, the angles of elevation are 60° and 30°. Find the height of the poles and distances from the point.

Solution:

Let OD = distance from one pole

Using equations:

3(80 − OD) = OD
OD = 60 m

Height of pole:

CD = 60 / √3
= 20√3 m

Other distance:

OB = 80 − 60
= 20 m

So, the height of poles is 20√3 m and distances are 20 m and 60 m.

FAQs

1. Where do I find the NCERT Solutions for Class 10 Maths Chapter 9?

Some Application of Trigonometry NCERT Solutions in Class 10, Chapter 9 can be easily downloaded from the ToppersSky platform. Students can access the app for topperssky to browse Chapter-specific answers, videos as well as detailed step-by-step instructions. The solutions are in a format that is easy to read which makes revision easy and efficient.

2. What can you do with studying in NCERT’s Solutions to Class 10 Chapter 9 of Maths?

This chapter assists students in understanding how to determine the size and distance of objects, without actually measuring them. Through understanding these concepts clearly students are able to confidently solve trigonometry-based questions in tests. It also enhances the ability to think logically and assists students perform better in tests at school and on board exams.

3. Is NCERT Answers in Grade 10 Mathematics Chapter 9 enough for board exams?

Yes, if students will have understood completely, have practiced lots of questions and really have good content knowledge, then they can rely on NCERT Solutions for exam preparation. After having completed all the tasks, students can increase their confidence by completing more practice problems and taking mock exams available on ToppersSky.

4. What does ToppersSky help make Chapter 9 more understandable?

ToppersSky employs Animation techniques for learning to teach geometric concepts in a visual manner. Students can view animated videos in 3D and 2D which clearly display the angles for elevation and depression as well as line of sight. Additionally, structured notebooks, mental maps and practice sets assist students improve their understanding quickly and rapidly.

5. What can students do to improve their skills of problem solving within this section?

Students can develop their skills by systematically working through step-by-step solutions. The process of answering questions through logical reasoning together with timed question completion will develop both speed and accuracy. ToppersSky offers guidance on how to write the answers properly in tests, which can help students achieve better marks.