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## 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.

**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)

Please click the link below to download CBSE Class 10 Mathematics Applications Of Trigonometry Worksheet Set E

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

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

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

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