SEE (Unit - 16) Trigonometry Height and Distance (Execise with Answers)

Trigonometry

Height and Distance- Part Two

Exercise with Answers:

1.      An observer sees the top of a tower at a distance of 28√3m from the point of observation on the ground level. If the angle of elevation of the tower is found to be 30°, find the height of the tower. 

Ans - 28 m

2.      An observer is measuring the angle of elevation of a tower of height 50√3m from the horizontal point 50m away from the foot of the tower. What angle will he measure? 

Ans-60

3.      A woman looks at the top of a tree which is 36m high from a point on the ground at an angle of 30° to the horizontal line. How far is she from the bottom of the tree?  

Ans- 36√3 m

4.      A man of height 1.5m observes the top of a telephone tower from a horizontal point 30m away from the bottom of the tower. If the angle of elevation of the tower is 60°, what will be the height of the tower? 

Ans- 53.46m

5.      A person looks at a pigeon on the ground level from his house of height 50m. If the pigeon be 50√3m away from the bottom of the house, what will be the angle of depression of the pigeon?  

 Ans- 30°

6.      A shadow of a man of height 5√3ft. is 15ft at 4 pm. What will be the length of the shadow of a pole which is three times higher than the man at the same time, i.e. 4pm?

Ans- 45m

7.      A man, 1.4m tall, is inspecting the behavior of a bird sitting at the top of a pole of the height 43.4m. If the man is standing 14√3m away from the bottom of the pole on horizontal level, at what angle is he looking at the bird?  

Ans- 60°

8.      A cat is focusing its eyes on a rat eating potatoes on the ground from a certain height. If the angle of depression is found to be 60° for the rat which is 12√3m away from the height of the cat, how high is the cat sitting at?  

Ans- 53.46m

9.      A poacher is targeting a dove sitting on the ground level from the roof of the house which is 45m high. If the dove be 45m away from the bottom of the house, at what angle should the poacher fix his catapult not to miss the target?  

Ans- 30°

10.   A tree of height 40m is situated on the bank of a river. If the angle of elevation of the tree observed from the opposite bank of the same river be 45°, what will be the breadth of the river?  

Ans- 45m

11.   A lamp post is erected at the centre of a circular pond of radius 12√3m and depth 16m. If the angle of elevation of the lamp post observed from a point on the edge of the pond is found to be 30°, find the height of the lamp post from the bottom of the pond. 

Ans- 60°

12.   An electric post is erected at the centre of a circular pond. The angle of elevation of the post of height 30√3m from the level of water is 60°. What will be the shortest distance between the centre and the circumference of the circular pond, if that angle of elevation is measured from a point of the circumference of the pond? 

Ans- 36m

13.   What will be the length of the shadow of a vertical pole of height 18√3m when the angle of elevation of the sun is 30°? 

Ans- 40m

14.   What will be the height of a vertical pole when the length of its shadow is 36√3m and the angle of elevation of the sun is 60°?  

Ans- 28m

15.   A tall tree of height 51m is broken because of the strong wind. If the broken part of the tree touches the ground level and makes an angle of 30° with the horizontal level, what will be the length of the broken and remaining parts of the tree? 

Ans- 30m

16.   A tall tree of height 60m is broken due to the strong wind. If the upper 40m broken part of the tree touches the level ground, calculate the angle made by the broken part with the horizontal line. Also, calculate the horizontal distance between the bottom of the tree and the point at which the broken part of the tree touches the ground level. 

Ans - 30, 20√3 m

17.   The angle of elevation of the top of a tree observed from the roof of a house which is 18m high is 30°. If the height of the tree be 38m, find the distance of the house from the bottom of the tree.  

Ans- 20√3 m

18.   A man of height 1.7m is observing a bird sitting at the top of a tree of height 53.7m at an angle of 30° with the horizontal direction. Find the distance between the man and the tree. 

Ans- 52√3 

19.   The angle of depression of a house of height 15m observed from the top of a tower is 60°. Find the distance between the house and the tower if the height of the tower is 30m. 

Ans- 5√3m 

20.   The angle of elevation of a pole of height 150√3m observed from the roof of a house is found to be 30°. If the distance between the house and the pole is 60m, find the height of the house. 

Ans- 130√3 m

21.   An observer of height 1.4m is observing the top of a telegraph tower of height 91.4m at a distance of 30√3m from the tower. Find the angle of elevation of the top of the tower.

Ans- 60°

22.   The angle of depression of a boat sailing on the ocean is observed from the top of a cliff. If the height of the cliff is 20√3m and the distance of the boat from the bottom of the cliff is 60m, what will be the angle of depression of the boat?  

Ans- 30°

23.   A ladder rests on the vertical wall at a height of 18m. If the lower end of the ladder is 6√3m away from the bottom of the wall, find the angle made by it with the ground level. Also, find the length of the ladder. 

Ans- 60, 12√3m

24.   A lamp post is erected inside the water of a circular pond. If the angle of elevation of the top of the lamp post observed from two opposite points of the circumference of the pond are 30° and 60° and the height of the post above the level of water is 21m, what will be the diameter of the circular pond? Also find the circumference of the pond. 

Ans- 28√3 m, 88√3 m

25.   From the roof of a house of 90m height, the top of a pillar of height 30m is observed at an angle of 45° with the horizontal. Find the distance between the house and the pillar.

Ans- 60m

26.   150m long cord of a kite has been unwound out by a boy who is flying it from a roof of a house of 20m height. If the angle of elevation of the kite be 30° from the roof of the house, find the height of the kite from the ground level. 

Ans- 95 m

27.   An electrical pole is erected at the centre of a circular pasture. If the height of the pole be 30√3m and its angle of elevation from the observer sitting on the circumference of the pasture be 30°, find the diameter and the circumference of the pasture. 

Ans- 180m, 565.71m