NCERT Solutions for Class 10 Maths Chapter 9: Trigonometry is one of the fundamental subjects that students learn in Class 10. This subject plays a vital role in higher 11th and 12th grades and future competitive exams. Therefore, academic experts at Embibe have curated the NCERT Solutions for Class 10 Maths Chapter 9 “Some Applications of Trigonometry” to help students in their board exams.
The NCERT Solutions for Class 10 Maths Chapter 9 Exercise 9.1 provided in this article will help students to get a detailed, step-by-step approach for solving the in-text questions. It shall also help students develop crucial problem-solving skills while strengthening their conceptual understanding. Further, the CBSE Class 10 Maths Solutions is available in PDF format for quick reference for students.
NCERT Solutions for Class 10 Maths Chapter 9: Some Applications of Trigonometry
Before getting into the details of CBSE Class 10 Maths Chapter 9 NCERT solutions, let us a have look at the topics in the chapter. Moreover, here we also provide an overview of the exercises involved in Chapter 9 Maths for Class 10. The exercises involved in CBSE Class 10 Maths Chapter 9 NCERT Solutions include NCERT Solutions for Class 10 Maths – Chapter 9, Exercise 9.1; NCERT Solutions for Class 10 Maths – Chapter 9, Exercise 9.2; and NCERT Solutions for Class 10 Maths – Chapter 9, Exercise 9.3. You can check various concepts discussed in each exercise are given in the table below:
In this section, students learn about the origins, and importance of Trigonometry through a general introduction to the subject.
Heights and Distance
In this section, students learn to calculate heights and distances using trigonometry. They are introduced to concepts like ‘line of sight’, ‘angle of elevation’ and ‘angle of depression.
The summary encapsulates the whole learnings of various applications of trigonometry.
NCERT Solutions for Class 10 Maths Chapter 9: Download PDF
Q: A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string. Solution: Consider the figure below,
Let A represents the position of the kite and the string is tied to point C on the ground. In △ABC sin60°=ABAC ⇒32=60AC ⇒AC=1203=403 m
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building. Solution:
Let us assume initially the boy was standing at S. After walking towards the building, he reached point T. In the figure, PQ = height of the building =30 m Height of the boy AS=BT=RQ=1.5 m PR=PQ-RQ=30 m-1.5 m=28.5 m In △PAR, tan30°=PRAR ⇒13=28.5AR ⇒AR=28.53 cm In △PRB, tan60°=PRBR ⇒3=28.5 BR ⇒BR=28.53=9.53 ST=AB=AR-BR=28.53-9.53=193 Hence, distance the boy walked towards the building =193 m
CBSE Class 10 Maths Chapter 9: Summary
Previously, we know that trigonometry is a branch of mathematics that deals with the relationships between sides and angles of triangles. We know how trigonometry plays a key role in solving numerous problems that exist in the real world. On one side, trigonometry is extensively used by astronomers for finding the distance between heavenly bodies like the sun, the moon, and the stars on the other side it has great applications in preparing maps, geography, engineering, and navigation.
In the Class 10 Maths Chapter 9 introduction, we will learn the use of trigonometry in the measurement of heights and distances which cannot be measured directly, i.e., finding the height of a tower, the distance between two objects, etc. Also, most probably for the first time, you will be introduced to a few important terms like Angle of Elevation, Angle of Depression, etc.
In this chapter, you will learn about some interesting ways to implement trigonometry and solve real-life problems. This chapter has only one exercise. The questions are based on real-life applications of trigonometry. You will have to visualize and mathematically represent it to solve the problems. Questions from this chapter are frequently asked in various competitive examinations. With little understanding of various terms used and the basics of trigonometry, one can easily solve the problems related to this chapter. If you have any doubts about the Chapter, NCERT Solutions by Embibe for Class 10 Maths Chapter 9 comes in handy. This allows the students to score good marks in their exams and boosts their confidence.
Practice Questions from CBSE NCERT Class 10 Maths Chapter 9
For your practice, a few important questions that could be asked in your Term II exam are given below along with their final answers. We hope that students will be able to solve these questions easily by referring to the concepts given in the solutions provided above. Students can check the CBSE Class 10 question bank released by the board to practice questions on a regular basis.
Q1. What is the angle of elevation of a cloud whose reflection is observed by a man who is standing on a platform 3 meters above the surface of a lake? Ans. The angle of elevation of the cloud is not equal to the angle of depression of its reflection.
Q2. When a man observing a tower moves 20 meters towards the tower, the angle of elevation of the top increases by 15°. Determine the height of a tower if the angle of elevation of the top of a tower from a certain point is given as 30°. Ans. The height of the tower is 10 (√3 + 1).
Q3. If the height of the tower is doubled, Calculate the angle of elevation of the top of the tower if the height of the tower is doubled. The angle of elevation of the top of a tower is given as 30°. Ans. The angle of elevation of the top of the tower will be less than 60°.
Q4. Find the angle of elevation of the Sun’s altitude if the length of the shadow of a vertical pole is equal to √3 times its height. Ans. The angle of elevation of the Sun’s altitude is 30°.
Q5. Calculate the height of a wall if a ladder makes an angle of 60° with it. The given ladder is 15 meters long and just reaches the top of the wall. Ans. The height of the wall is 7.5 m.
Q6. Calculate the height of a plane above the ground if it makes an angle of elevation of 60° and is at a distance of 12 km from the point of observation. Ans. The height of a plane above the ground is 6√3 m.
Q7. Determine the height of therock if the angles of elevation of the top of therock from the top and bottom of a tower of height 100 m are 30° and 45°, respectively. Ans. The height of the rock is 50(3 + √3) m.
Q8. Calculate the angle of elevation of the top of a tower of the height of 22 meters from the eye of an observer if the given height of the observer is 1.5 meters Ans. The angle of elevation of the top of a tower is 45°.
Key Features of Embibe’s Class 10 Maths NCERT Solutions of Chapter 9
For the ease of students, the academic experts and teachers of Embibe have compiled the solutions in a simple and lucid language.
All the answers to questions and exercises in NCERT 10th Maths textbook are included in these solutions.
With the help of Embibe’s NCERT solutions for the chapter ‘Some Applications Of Trigonometry’, you can easily learn the real-life applications of trigonometry and the concepts of the angle of deviation, angle of elevation, angle of depression, and line of sight.
Students can become familiar with different types of questions asked in the exams by following NCERT solutions by Embibe.
Embibe’s NCERT solutions are very useful for completing homework and assignments.
The best feature of NCERT solutions by Embibe is that they are available for free.
Practice 10th Maths Questions with Embibe
We have now provided you with all CBSE Class 10 Maths NCERT solutions in Chapter 9. Refer to these solutions as you solve the problems to have a better understanding. You can also take free Applications of Trigonometry mock test on Embibe. This mock test will definitely help you in your preparation for the final exams.
We also advise 10th-grade students to make use of other resources offered by Embibe to boost their scores. Students can solve CBSE Class 10 Practice Questions or take Class 10 Mock Tests on Embibe. They can also download the NCERT Class 10 Textbook for all Class 10 subjects at Embibe. All these resources are available for free and can be accessed without any sign-up formalities.
FAQs on NCERT Class 10 Maths Solutions Chapter 9
Q1. How many exercises are there in Chapter 9 of CBSE Class 10 Maths? Ans.Chapter 9 of CBSE Class 10 Maths has one exercise – Exercise 9.1 – at the end of the chapter containing 16 questions covered in the first two parts.
Q2. What are the important points to study in Class 10 Maths NCERT Chapter 9? Ans.The important points to study in Class 10 Maths NCERT Chapter 9 include: – Fundamental Basics Of Trigonometry Applications – The History Behind Trigonometry – Concepts On Height And Distance – The Calculation Methods For Heights And Distance – The Trigonometry Ratios And Angle Tables For The Ratios – The Study About The Line Of Sight – Angle Of Elevation, Horizontal Level – Angle Of Depression
Q3. Is NCERT Solutions for Class 10 Maths Chapter 9 sufficient for CBSE second term exams? Ans. Yes, once you have solved all the questions in Maths chapter 9 NCERT solutions Class 10, you would be able to score well in your CBSE board exam.
Q4. Where can I download CBSE Class 10 Maths NCERT solutions chapter 9? Ans. You can download the Class 10 NCERT Maths chapter 9 solutions PDF from Embibe’s website for free. The links are provided in the above article.
Q5. What are the real-life applications of referring to NCERT Solutions for Class 10 Chapter 9Maths? Ans. The concepts and methods are given in NCERT Solutions for Class 10 Chapter 9 Maths have several real-life applications such as finding the height and distance of different objects without measuring. Moreover, students will be able to answer all the questions based on trigonometry in their CBSE Term II exams.
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