EduSahara™ Worksheet

Question 1

1.

From a point 120 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 cliff.

(i)

66.29 m
(ii)

74.29 m
(iii)

64.29 m
(iv)

72.29 m
(v)

69.29 m

Question 2

2.

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 60° and 45° respectively. Find the height of the pillar.

(i)

73.21 m
(ii)

78.21 m
(iii)

76.21 m
(iv)

70.21 m
(v)

68.21 m

Question 3

3.

The angles of depression of two boats from the top of a cliff 180 m high are 60° and 30° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

193.85 m
(ii)

224.85 m
(iii)

207.85 m
(iv)

195.85 m
(v)

222.85 m

Question 4

4.

The angles of depression of two boats from the top of a cliff 90 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

232.89 m
(ii)

223.89 m
(iii)

260.89 m
(iv)

245.89 m
(v)

259.89 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 8 min for the angle of depression to change from 45° to 60°, how soon after this, will the car reach the observation tower?

(i)

9 min 55 sec
(ii)

7 min 54 sec
(iii)

10 min 56 sec
(iv)

11 min 57 sec
(v)

12 min 58 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 45° to 30°. Find the height of the tower .

(i)

15.49 m
(ii)

23.49 m
(iii)

25.49 m
(iv)

17.49 m
(v)

20.49 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 45° and 60° and the distance between them is 155 m , find the height of the cliff.

(i)

103.27 m
(ii)

93.27 m
(iii)

101.27 m
(iv)

95.27 m
(v)

98.27 m

Question 8

8.

A man in a boat rowing away from a lighthouse 40 m high, takes 4.5 min to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat.

(i)

7.17 m/sec
(ii)

2.17 m/sec
(iii)

1.17 m/sec
(iv)

0.17 m/sec
(v)

8.17 m/sec

Question 9

9.

A man 1.9 m tall stands at a distance of 3.3 m from a lamp post and casts a shadow of 7.5 m on the ground. Find the height of the lamp post .

(i)

1.74 m
(ii)

4.74 m
(iii)

2.74 m
(iv)

3.74 m
(v)

0.74 m

Question 10

10.

Two vertical poles are on either side of a road. A 37 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 60° with the pole and when it is turned to rest against another pole, it makes an angle of 45° with the road. Find the width of the road.

(i)

47.66 m
(ii)

49.66 m
(iii)

39.66 m
(iv)

44.66 m
(v)

41.66 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)

∠c
(iii)

∠f
(iv)

∠d

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)

∠d
(ii)

∠f
(iii)

∠g
(iv)

∠e

Assignment Key