NCERT solutions for class 10 Maths chapter 9 some applications of trigonometry includes topics like Introduction, heights and distances, and more. Get the NCERT textbook solutions PDFs here.
The NCERT solutions for class 10 Maths chapter 9 belong to unit 5, Trigonometry, which has a weightage of 12 marks in the CBSE class 10 Maths examination. The NCERT solutions for class 10 maths chapter 9 some applications of trigonometry discusses finding the height and distance of various objects without measuring them directly. It is an important chapter in class 10 divided into 3 major sections.
NCERT solutions for class 10 for Trigonometry enables students to revise all formulas and concepts. All the candidates must be well versed with the previous papers, which builds the foundation for this topic. Moreover, the questions from this NCERT solution for class 10 Maths chapter 9 are mostly based on heights, distances, and angles of depression.
Table of Contents
- NCERT Solutions for Class 10 Maths Chapter 9 Download PDF
- NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Important Questions
- NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Sub- Topics
- List of Formulas in NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry
- Key Features of NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry
NCERT Solutions for Class 10 Maths Chapter 9 Download PDF
The chapter 9 class 10 Maths covers all the vital chapters and provides chapter-wise solutions. These NCERT solutions are helpful for the students to clarify their doubts and provide a strong foundation for every concept.
| NCERT Solutions For Class 10 Maths Chapter 9 Some Applications of Trigonometry | Download |
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry - Important Questions
The detailed questions and solutions for the exercise 9.1 class 10 is mentioned below for students reference.
Ex 9.1 Class 10 Maths Question 1.
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°.
Solution:
Ex 9.1 Class 10 Maths Question 2.
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 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.
Solution:
Ex 9.1 Class 10 Maths Question 3.
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3 m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
Solution:
Ex 9.1 Class 10 Maths Question 4.
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. Find the height of the tower.
Solution:
Ex 9.1 Class 10 Maths Question 5.
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:
Ex 9.1 Class 10 Maths Question 6.
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:
Ex 9.1 Class 10 Maths Question 7.
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.
Solution:
Ex 9.1 Class 10 Maths Question 8.
A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
Solution:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Sub- Topics
The following table has been provided to give the students a glimpse at the subtopics under the chapter 9 class 10 Maths on Applications of Trigonometry.
| Serial Number | Important Topics |
| 1 | Introduction |
| 2 | Heights and Distances |
| 3 | Summary |
Line of sight and horizontal level
- Line of sight is the line from the eye of the observer to the point of the object viewed by the observer.
- Horizontal level is a horizontal line through the eye of the observer.
The angle of elevation is the angle formed by the line of sight with the horizontal level.
- Angle of elevation is relevant for objects that are above horizontal level.
The angle of depression is the angle that is formed between the line of sight and the horizontal level.
- Angle of depression is is relevant for objects that are below horizontal level.
Calculating Heights and Distances: To calculate the heights and distances, we make use of trigonometric ratios.
Step 1: Draw a line diagram that corresponds to the given problem.
Step 2: Mark all the known angles, heights, and distances. Denote the unknown lengths by variables such as x,y, etc.
Step 3: Use the values of different trigonometric ratios of the angles to find the unknown lengths from the given lengths.
List of Formulas in NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry
Most of the questions in the chapter 9 class 10 Maths lesson are solved using trigonometric ratios such as tan, cos, sin, etc, as well as certain identities. The candidates must be well versed with these formulas to build the foundation for this topic.
- Sin A= Perpendicular/ Hypotenuse
- Cosec A= Hypotenuse / Perpendicular
- Cos A = Base/ Hypotenuse
- Sec A= Hypotenuse/ Base
- Tan C = Perpendicular/ Base
- Cot C= Base/ Perpendicular
Key Features of NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry
This chapter in NCERT solution is useful for the CBSE class 10 board. The questions are designed in such a way as to improve the problem-solving abilities of the students. Some of the important features of the application of Trigonometry are mentioned below.
- The solutions are designed by subject experts.
- Access to chapter-wise questions and answers.
- Valuable guidance for the students to prepare for the CBSE exams.
- The solutions are explained in detailed procedure.
- Easy access to all the exercise solutions.
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