EduSahara™ Worksheet

Question 1

1.

From a point 100 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 45° and 30° respectively. Find the height of the cliff.

(i)

60.74 m
(ii)

54.74 m
(iii)

62.74 m
(iv)

52.74 m
(v)

57.74 m

Question 2

2.

From a point 90 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 30° respectively. Find the height of the pillar.

(i)

106.92 m
(ii)

103.92 m
(iii)

85.92 m
(iv)

101.92 m
(v)

120.92 m

Question 3

3.

The angles of depression of two boats from the top of a cliff 200 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

139.42 m
(ii)

124.42 m
(iii)

171.42 m
(iv)

160.42 m
(v)

146.42 m

Question 4

4.

The angles of depression of two boats from the top of a cliff 120 m high are 60° and 30° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

260.14 m
(ii)

303.14 m
(iii)

263.14 m
(iv)

294.14 m
(v)

277.14 m

Question 5

5.

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 6 min for the angle of depression to change from 30° to 60°, how soon after this, will the car reach the observation tower?

(i)

5 min 8 sec
(ii)

4 min 6 sec
(iii)

2 min 4 sec
(iv)

3 min 0 sec
(v)

0 min 2 sec

Question 6

6.

The shadow of a vertical tower BA on a level ground is increased by 15 m, when the altitude of the sun changes from 60° to 30°. Find the height of the tower .

(i)

9.99 m
(ii)

17.99 m
(iii)

15.99 m
(iv)

7.99 m
(v)

12.99 m

Question 7

7.

A boy standing on a vertical cliff in a jungle observes two rest houses in line with him on opposite sides deep in the jungle below. If their angles of depression are 60° and 30° and the distance between them is 105 m , find the height of the cliff.

(i)

45.47 m
(ii)

48.47 m
(iii)

40.47 m
(iv)

42.47 m
(v)

50.47 m

Question 8

8.

A man in a boat rowing away from a lighthouse 25 m high, takes 2.5 min to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat.

(i)

1.19 m/sec
(ii)

0.19 m/sec
(iii)

7.19 m/sec
(iv)

8.19 m/sec
(v)

2.19 m/sec

Question 9

9.

A man 1.3 m tall stands at a distance of 8.5 m from a lamp post and casts a shadow of 8.4 m on the ground. Find the height of the lamp post .

(i)

0.62 m
(ii)

2.62 m
(iii)

3.62 m
(iv)

4.62 m
(v)

1.62 m

Question 10

10.

Two vertical poles are on either side of a road. A 38 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 45° with the pole and when it is turned to rest against another pole, it makes an angle of 30° with the road. Find the width of the road.

(i)

59.78 m
(ii)

64.78 m
(iii)

62.78 m
(iv)

56.78 m
(v)

54.78 m

Question 11

11.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?

(i)

∠e
(ii)

∠g
(iii)

∠d
(iv)

∠f

Question 12

12.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?

(i)

∠f
(ii)

∠d
(iii)

∠c
(iv)

∠e

Assignment Key