SAMACHEER KALVI CLASS 10 TRIGONOMETRY

 SAMACHEER KALVI CLASS 10

TRIGONOMETRY

IMPORTANT CONCEPT BASED QUESTIONS

TOTAL NUMBER OF QUESTIONS: 18

1. Prove the following identities.

(i) cot θ + tan θ = sec θ cosec θ
(ii) tan4 θ + tan2 θ = sec4 θ – sec2 θ

2. Prove the following identities.
(i) sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1

3.  If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q (p2 – 1) = 2 p

4. Prove the following identities.

5.  If sin θ + cos θ = 3–√, then prove that tan θ + cot θ = 1.

6. Find 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 a tower of height 10 3–√ m.

7. To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and if he is 5 m away from the wall, what is the height of the window? (3–√ = 1.732)

8. The top of a 15 m high tower makes an angle of elevation of 60° with the bottom of an electronic pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?

9. A vertical pole fixed to the ground is divided in the ratio 1:9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 25 m away from the base of the pole, what is the height of the pole?

10. From the top of a rock 50 3–√ m high, the angle of depression of a car on the ground is observed to be 30°. Find the distance of the car from the rock.

11.  An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are 60° and 30° respectively. Find the distance between the two boats. (3–√ = 1.732)

12. From the top of a lighthouse, the angle of depression of two ships on the opposite sides of it are observed to be 30° and 60°. If the height of the lighthouse is h meters and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is 4h/√3 m.

13. The horizontal distance between two buildings is 70 m. The angle of depression of the top of the first building when seen from the top of the second building is 45°. If the height of the second building is 120 m, find the height of the first building.

 

14. From the top of a tree of height 13 m the angle of elevation and depression of the top and bottom of another tree are 45° and 30° respectively. Find the height of the second tree, (3–√ = 1.732)

15. The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30° . If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiations control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms.

16. Three villagers A, B and C can see each other across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30°. Calculate:
(i) the vertical height between A and B.
(ii) the vertical height between B and C. (tan 20° = 0 .3640, 3–√ = 1. 732)

17. The angles of elevation and depression of the top and bottom of a lamp post from the top of a 66 m high apartment are 60° and 30° respectively. Find
(i) The height of the lamp post.
(ii) The difference between height of the lamp post and the apartment.
(iii) The distance between the lamp post and the apartment. (3–√ = 1.732)

18. A man is standing on the deck of a ship, which is 40 m above water level. He observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30° . Calculate the distance of the hill from the ship and the height of the hill. (3–√ = 1.732)