Some Applications of Trigonometry
1. A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 5m. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are 60° and 30° respectively. Find the height of the tower and the distance of the point from base of the tower.
View AnswerAns.
2. A man standing on the deck of a ship, which is 10 m above the water level, 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 height of the hill.
View AnswerAns.
3. A tree breaks down due to storm and the broken part bends, so that the top of the tree touches the ground making an angle of 30° with it. The distance from the foot of the tree to the point where the top touches the ground is 8 metres. Find the height of the tree before it was broken.
View AnswerAns.
4. A kite is attached to a string. Assuming that there is no slack in the string, find the height of the kite above the level of the ground, if the length of the string is 54 m and it makes an angle of 30° with the ground.
View AnswerAns. 27 m
5. In the given figure, the angle of elevation of the top of a tower from a point C on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
View Answer
Ans. 10√3 m
6. The ratio of the length of a vertical rod and the length of its shadow is 1 : 3 . Find the angle of elevation of the sun at that moment?
View AnswerAns. 30°
7. An electrician has to repair an electric fault on a pole of height 4 m. He needs to reach a point 1.3 m below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use which, when inclined at an angle of 60° to the horizontal would enable him to reach the required position?
Ans.
8. The rod AC of a TV disc antenna is fixed at right angles to the wall AB and a rod CD is supporting the disc as shown in the figure. If AC = 1.5 m long and CD = 3 m, find
(a) tan q
(b) sec q + cosec q
Ans.
9. The angle of depression of the top and bottom of a tower as seen from the top of a 60√3m high cliff are 45° and 60° respectively. Find the height of the tower.
View AnswerAns.
10. From the top of a tower 50 m high, the angle of depression of the top of a pole is 45° and from the foot of the pole, the angle of elevation of the top of the tower is 60°. Find the height of the pole if the pole and tower stand on the same plane.
View AnswerAns.
11. The angle of depression from the top of a tower of a point A on the ground is 30°. On moving a distance of 20 m from the point A towards the foot of the tower to the point B, the angle of elevation of the top of the tower from the point B is 60°. Find the height of the tower and its distance from the point A.
View AnswerAns.
12. The given figure shows a statue, 1.6 m tall, standing on the top of pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.
Ans. (0.8) ( 3 + 1) m
13. The angles of elevation of the top of a tower from two points at a distance of 6 m and 13.5 m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.
Ans.
14. Two ships are there in the sea on either side of a lighthouse in such a way that the ships and the lighthouse are in the same straight line. The angles of depression of two ships as observed from the top of the lighthouse are 60° and 45°. If the height of the lighthouse is 200 m, find the distance between the two ships.
View AnswerAns.
15. The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds the angle of elevation becomes 30°. If the aeroplane is flying at a constant height of 3000 3 m, find the speed of the aeroplane.
View AnswerAns.
16. From a point P on the ground, the angle of elevation of the top of a 10 m tall building is 30°. A flagstaff is fixed at the top of the building and the angle of elevation of the top of the flagstaff from the point P is 45°. Find the length of the flagstaff and the distance of building from the point P.
View AnswerAns.
17. From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Determine the height of the tower.
View AnswerAns.
18. A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards him. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?
View AnswerAns. 16.39 mins
19. Two men on either side of a 75 m high building and in line with base of building observe the angles of elevation of the top of the building as 30° and 60°. Find the distance between the two men.
View AnswerAns.
20. As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
View AnswerAns.
21. The angles of depression of the top and bottom of a 50 m high building from the top of a tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower and the building.
View AnswerAns.
22. A man in a boat rowing away from a lighthouse 100 m high takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat in metres per minute.
View AnswerAns.
23. Two poles of equal heights are standing opposite to each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distances of the point from the poles.
View AnswerAns.
24. At the foot of a mountain, the angle of elevation of its summit is 45°. After ascending 1 km towards the mountain up an incline of 30°, the elevation changes to 60°. Find the height of the mountain.
View AnswerAns. 1.366 km
25. The angles of depression of the top and bottom of a building 50 metres high as observed from the top of a tower are 30° and 60°, respectively. Find the height of the tower and also the horizontal distance between the building and the tower.
View AnswerAns.
