NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex 9.1

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex 9.1 are part of NCERT Solutions for Class 10 Maths. Here are we have given Chapter 9 Some Applications of Trigonometry Class 10 NCERT Solutions Ex 9.1.

Trigonometry can be used in many ways in the things around us like we can use it for calculating the height and distance of some objects without calculating them actually. We are provides free comprehensive chapter wise class 10 Mathematics notes with proper images & diagram. Here you will find all the answers to the NCERT textbook questions of Chapter 9 Some Applications of Trigonometry.

BoardCBSE
TextbookNCERT
ClassClass 10
SubjectMaths
ChapterChapter 9
Chapter NameSome Applications of Trigonometry
ExerciseEx 9.1
Number of Questions Solved16
CategoryNCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex 9.1

NCERT Solutions for Class 10 Maths

Page No: 203

Question http://1.bp.blogspot.com/-Zf9a-LDpwyM/VXv9xUXApEI/AAAAAAAAAt8/PecVykpMrWo/s1600/ch-11-some-applications%2Bof-trigo-1.PNG1. 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°.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 1

Solution:
In the Figure, AB is the pole.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 2

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:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 3
Let AC be the original tree and be the broken part which makes an angle of 30o with the ground.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 4

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:
In the two figures, AC and PR are the slides for younger and elder children respectively
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 5

Page No: 204

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:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 6

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:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 7
Let A be the position of the kite and the string is tied to point C on ground.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 8

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

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:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 10
Let BC be the building, AB be the transmission tower, and D be the point on ground from where elevation angles are to be measured.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 11

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 12
Let AB be the statue, BC be the pedestal and D be the point on ground from where elevation angles are to be measured.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 13

Question 9. The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

Solution:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 14

Question 10. Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

Solution:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 15

Question 11. A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 16

Solution:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 17

Question 12. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Solution:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 18

Question 13. As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Solution:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 19
Let AB be the lighthouse and the two ships be at point C and D respectively.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 20

Page No: 205

Question 14. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m
from the ground. The height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.

Solution:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 21
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 22

Question 15. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

Solution:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 23
Let AB be the tower. C is the original position of the car which changes to D after six seconds.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 24

Question 16. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

Solution:
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 25
Let AQ be the tower and R, S respectively be the points which are 4m, 9m away from base of tower.
NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry 26
As the height can not be negative, the height of the tower is 6 m.

We hope the NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex 9.1 help you. If you have any query regarding NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex 9.1, drop a comment below and we will get back to you at the earliest.

Leave a Comment