# NCERT Mathematics Class 10 Exemplar Ch 8 Introduction to Trigonometry and Its Applications Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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EXERCISE 8.4

1. If , then prove that .

2. Prove that .

3. The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.

Answer:

4. If 1 + , then prove that .

5. Given that then prove that

6. The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is

7. The shadow of a tower standing on a level plane is found to be 50 m longer when Sun՚s elevation is 30° than when it is 60°. Find the height of the tower.

Answer:

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

9. If then prove that .

10. If and , then prove that .

11. If a , then prove that a .

12. Prove that

13. The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the other tower.

Answer:

14. From the top of a tower h m high, the angles of depression of two objects, which are in line with the foot of the tower are α and . Find the distance between the two objects.

Answer:

15. A ladder rests against a vertical wall at an inclination α to the horizontal. Its foot is pulled away from the wall through a distance p so that its upper end slides a distance q down the wall and then the ladder makes an angle β to the horizontal. Show that

16. The angle of elevation of the top of a vertical tower from a point on the ground is 60o . From another point 10 m vertically above the first, its angle of elevation is 45o . Find the height of the tower.

Answer:

17. A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. Prove that the height of the other house is metres.

18. The lower window of a house is at a height of above the ground and its upper window is vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be and , respectively. Find the height of the balloon above the ground.

Answer: