# CBSE Class 10 Mathematics Applications Of Trigonometry Worksheet Set E

Read and download free pdf of CBSE Class 10 Mathematics Applications Of Trigonometry Worksheet Set E. Students and teachers of Class 10 Mathematics can get free printable Worksheets for Class 10 Mathematics Chapter 9 Applications of Trigonometry in PDF format prepared as per the latest syllabus and examination pattern in your schools. Class 10 students should practice questions and answers given here for Mathematics in Class 10 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 10 Mathematics Worksheets prepared by school teachers as per the latest NCERT, CBSE, KVS books and syllabus issued this academic year and solve important problems with solutions on daily basis to get more score in school exams and tests

## Worksheet for Class 10 Mathematics Chapter 9 Applications of Trigonometry

Class 10 Mathematics students should refer to the following printable worksheet in Pdf for Chapter 9 Applications of Trigonometry in Class 10. This test paper with questions and answers for Class 10 will be very useful for exams and help you to score good marks

### Class 10 Mathematics Worksheet for Chapter 9 Applications of Trigonometry

SOME APPLICATIONS OF TRIGONOMETRY

Q.- From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 30º. The angle of elevation of the top of a water tank (on the top of the tower) is 45º. Find the
(i) height of the tower
(ii) the depth of the tank.

Sol. Let BC be the tower of height h metre and CD be the water tank of height h1 metre.
Let A be a point on the ground at a distance of 40 m away from the foot B of the tower.

Q.- Two stations due south of a leaning tower which leans towards the north are at distance a and b from its foot. If α, β be the elevations of the top of the tower from these stations, prove that its inclination θ to the horizontal is given by
Q.- If the angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake is β,prove that the height of the cloud is

Q.- There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are points directly opposite to each other on two banks, and in line with the tree. If the angles of elevation of the top of the tree from P and Q are respectively 30º and 45º, find the height of the tree.

Q.- The angle of elevation of a cliff from a fixed point is θ. After going up a distance of k metres towards the top of cliff at an angle of Φ, it is found that the angle of elevation is α. Show that the height of the cliff is

HEIGHT AND DISTANCES

KEY POINTS

Line of sight

Line segment joining the object to the eye of the observer is called the line of sight.

Angle of elevation

When an observer sees an object situated in upward direction, the angle formed by line of sight with horizontal line is called angle of elevation.

Angle of depression

When an observer sees an object situated in downward direction the angle formed by line of sight with horizontal line is called angle of depression.

LEVEL- I

1. A pole 6cm high casts a shadow 2

m long on the ground, then find the sun’s elevation?

2. If length of the shadow and height of a tower are in the ratio 1:1. Then find the angle of elevation.

3. An observer 1.5m tall is 20.5 metres away from a tower 22m high. Determine the angle of elevation of the top of the tower from the eye of the observer.

4. A ladder 15m long just reaches the top of vertical wall. If the ladder makes an angle 600 with the wall, find the height of the wall

5. In a rectangle ABCD, AB =20cm BAC=600 then find the length of the side AD.

6. Find the angle of elevation of the sun’s altitude when the height of the shadow of a vertical pole is equal to its height:

7. From a point 20m away from the foot of a tower, the angle of elevation of top of the tower is 30°, find the height of the tower.

8. In the adjacent figure, what are the angles of elevation and depression of the top and bottom of

a pole from the top of a tower h m high:

Ans450, 600

LEVEL -II

9. The length of the shadow of a pillar is √3 times its height. Find the angle of elevation of the source of light.

10. A vertical pole 10m long casts a shadow 10√3m long. At the same time tower casts a shadow 90m long. Determine the height of the tower.

11. A ladder 50m long just reaches the top of a vertical wall. If the ladder makes an angle of 600 with the wall, find the height of the wall.

12. Two poles of height 6m and 11m stands vertically on the ground. If the distance between their feet is 12m. Find the distance between their tops.

13. The shadow of tower, when the angle of elevation of the sun is 45o is found to be 10m longer than when it is 60o. Find the height of the tower.

LEVEL –III

14. The angle of depression of the top and bottom of a tower as seen from the top of a 100m high cliff are 300 and 600 respectively. Find the height of the tower.

15. From a window (9m above ground) of a house in a street, the angles of elevation and depression of the top and foot of another house on the opposite side of the street are 300 and 600 respectively. Find the height of the opposite house and width of the street.

16. From the top of a hill, the angle of depression of two consecutive kilometer stones due east are found to be 300 and 450. Find the height of the hill.

17. Two poles of equal heights are standing opposite each other on either side of the road, which is 80m wide. From a point between them on the road the angles of elevation of the top of the poles are 60◦ and 30◦. Find the heights of pole and the distance of the point from the poles.

18. The angle of elevation of a jet fighter from a point A on the ground is 600. After a flight of 15 seconds, the angle of elevation changes to 30◦. If the jet is flying at a speed of 720km/ hr, find the constant height at which the jet is flying.

19. A window in a building is at a height of 10m above the ground. The angle of depression of a point P on the ground from the window is 300. The angle of elevation of the top of the building from the point P is 600. Find the height of the building.

20. A boy, whose eye level is 1.3m from the ground, spots a balloon moving with the wind in a horizontal line at same height from the ground. The angle of elevation of the balloon from the eyes of the boy at any instant is 600. After 2 seconds, the angle of elevation reduces to 300 if the speed of the wind at that moment is 29 m/s, then find the height of the balloon from the ground.

21. A man on the deck on a ship 14m above water level observes that the angle of elevation of the top of a cliff is 600and the angle of depression of the base of the cliff is 300. Calculate the distance of the cliff from the ship and the height of the cliff.

22. A tower is 50m high. It’s shadow is x m shorter when the sun’s altitude is 45o than when it is 30o . Find x correct to the nearest 10.

SELF EVALUATION/HOTS

23. An airplane when flying at a height of 3125m from the ground passes vertically below another Plane at an instant when the angle of elevation of the two planes from the same point on the ground are 30°and 60° respectively. Find the distance between the two planes at that instant.

24. From the top of a building 60m high, the angels of depression of the top and bottom of a vertical lamp post are observed to be 30° and 60°respectively. Find [I] horizontal distance between the building and the lamp post [ii] height of the lamp post.

25. A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h m.At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are, respectively. Prove that the height of the tower is

26. The angle of elevation of a cloud from a point 60m above a lake is 30◦ and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake.

27. A round balloon of radius r subtends on angle α at the eye of the observer whose angle of elevation of centre is β . Prove that the height of the Centre of the balloon is (r sin β. Cosec α/2)

28. . A person standing on the bank of a river observes that the angle of elevation of top of building of an organization working for conservation of wild life. Standing on the opposite bank is 60o. When he moves 40m away from the bank, he finds the angle of elevation to be 30o. Find the height of the building and width of the river.

(a) Why do we need to conserve the wild life?

(b) Suggest some steps that can be taken to conserve wild life.

Activities

a. To make mathematical instrument eliminator ( or Sextant) for measuring the angle of elevation and depression of an object

b. To Calculate the height of an object making use of Clinometer ( or Sextant)

## More Study Material

### CBSE Class 10 Mathematics Chapter 9 Applications of Trigonometry Worksheet

We hope students liked the above worksheet for Chapter 9 Applications of Trigonometry designed as per the latest syllabus for Class 10 Mathematics released by CBSE. Students of Class 10 should download in Pdf format and practice the questions and solutions given in the above worksheet for Class 10 Mathematics on a daily basis. All the latest worksheets with answers have been developed for Mathematics by referring to the most important and regularly asked topics that the students should learn and practice to get better scores in their class tests and examinations. Studiestoday is the best portal for Class 10 students to get all the latest study material free of cost.

### Worksheet for Mathematics CBSE Class 10 Chapter 9 Applications of Trigonometry

Expert teachers of studiestoday have referred to the NCERT book for Class 10 Mathematics to develop the Mathematics Class 10 worksheet. If you download the practice worksheet for one chapter daily, you will get higher and better marks in Class 10 exams this year as you will have stronger concepts. Daily questions practice of Mathematics worksheet and its study material will help students to have a stronger understanding of all concepts and also make them experts on all scoring topics. You can easily download and save all revision worksheet for Class 10 Mathematics also from www.studiestoday.com without paying anything in Pdf format. After solving the questions given in the worksheet which have been developed as per the latest course books also refer to the NCERT solutions for Class 10 Mathematics designed by our teachers

#### Chapter 9 Applications of Trigonometry worksheet Mathematics CBSE Class 10

All worksheets given above for Class 10 Mathematics have been made as per the latest syllabus and books issued for the current academic year. The students of Class 10 can be rest assured that the answers have been also provided by our teachers for all worksheet of Mathematics so that you are able to solve the questions and then compare your answers with the solutions provided by us. We have also provided a lot of MCQ questions for Class 10 Mathematics in the worksheet so that you can solve questions relating to all topics given in each chapter. All study material for Class 10 Mathematics students have been given on studiestoday.

#### Chapter 9 Applications of Trigonometry CBSE Class 10 Mathematics Worksheet

Regular worksheet practice helps to gain more practice in solving questions to obtain a more comprehensive understanding of Chapter 9 Applications of Trigonometry concepts. Worksheets play an important role in developing an understanding of Chapter 9 Applications of Trigonometry in CBSE Class 10. Students can download and save or print all the worksheets, printable assignments, and practice sheets of the above chapter in Class 10 Mathematics in Pdf format from studiestoday. You can print or read them online on your computer or mobile or any other device. After solving these you should also refer to Class 10 Mathematics MCQ Test for the same chapter.

#### Worksheet for CBSE Mathematics Class 10 Chapter 9 Applications of Trigonometry

CBSE Class 10 Mathematics best textbooks have been used for writing the problems given in the above worksheet. If you have tests coming up then you should revise all concepts relating to Chapter 9 Applications of Trigonometry and then take out a print of the above worksheet and attempt all problems. We have also provided a lot of other Worksheets for Class 10 Mathematics which you can use to further make yourself better in Mathematics

Where can I download latest CBSE Printable worksheets for Class 10 Mathematics Chapter 9 Applications of Trigonometry

You can download the CBSE Printable worksheets for Class 10 Mathematics Chapter 9 Applications of Trigonometry for latest session from StudiesToday.com

Can I download the Printable worksheets of Chapter 9 Applications of Trigonometry Class 10 Mathematics in Pdf

Yes, you can click on the links above and download Printable worksheets in PDFs for Chapter 9 Applications of Trigonometry Class 10 for Mathematics

Are the Class 10 Mathematics Chapter 9 Applications of Trigonometry Printable worksheets available for the latest session

Yes, the Printable worksheets issued for Class 10 Mathematics Chapter 9 Applications of Trigonometry have been made available here for latest academic session

How can I download the Class 10 Mathematics Chapter 9 Applications of Trigonometry Printable worksheets

You can easily access the links above and download the Class 10 Printable worksheets Mathematics Chapter 9 Applications of Trigonometry for each chapter

Is there any charge for the Printable worksheets for Class 10 Mathematics Chapter 9 Applications of Trigonometry

There is no charge for the Printable worksheets for Class 10 CBSE Mathematics Chapter 9 Applications of Trigonometry you can download everything free

How can I improve my scores by solving questions given in Printable worksheets in Class 10 Mathematics Chapter 9 Applications of Trigonometry

Regular revision of practice worksheets given on studiestoday for Class 10 subject Mathematics Chapter 9 Applications of Trigonometry can help you to score better marks in exams

Are there any websites that offer free test sheets for Class 10 Mathematics Chapter 9 Applications of Trigonometry

Yes, studiestoday.com provides all latest NCERT Chapter 9 Applications of Trigonometry Class 10 Mathematics test sheets with answers based on the latest books for the current academic session

Can test papers for Class 10 Mathematics Chapter 9 Applications of Trigonometry be accessed on mobile devices

Yes, studiestoday provides worksheets in Pdf for Chapter 9 Applications of Trigonometry Class 10 Mathematics in mobile-friendly format and can be accessed on smartphones and tablets.

Are worksheets for Chapter 9 Applications of Trigonometry Class 10 Mathematics available in multiple languages

Yes, worksheets for Chapter 9 Applications of Trigonometry Class 10 Mathematics are available in multiple languages, including English, Hindi