# 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.

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.

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.

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.

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.