EduSahara™ Worksheet

Question 1

1.

From a point 60 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 cliff.

(i)

65.00 m
(ii)

63.00 m
(iii)

57.00 m
(iv)

55.00 m
(v)

60.00 m

Question 2

2.

From a point 110 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)

102.02 m
(ii)

123.02 m
(iii)

145.02 m
(iv)

127.02 m
(v)

133.02 m

Question 3

3.

The angles of depression of two boats from the top of a cliff 200 m high are 60° and 45° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

84.52 m
(ii)

87.52 m
(iii)

81.52 m
(iv)

79.52 m
(v)

89.52 m

Question 4

4.

The angles of depression of two boats from the top of a cliff 130 m high are 30° and 45° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

355.17 m
(ii)

342.17 m
(iii)

329.17 m
(iv)

373.17 m
(v)

358.17 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 14 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?

(i)

19 min 8 sec
(ii)

18 min 12 sec
(iii)

20 min 14 sec
(iv)

22 min 16 sec
(v)

16 min 11 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)

12.99 m
(ii)

15.99 m
(iii)

7.99 m
(iv)

9.99 m
(v)

17.99 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 45° and 60° and the distance between them is 200 m , find the height of the cliff.

(i)

132.80 m
(ii)

103.80 m
(iii)

141.80 m
(iv)

126.80 m
(v)

122.80 m

Question 8

8.

A man in a boat rowing away from a lighthouse 50 m high, takes 1 min to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat.

(i)

7.96 m/sec
(ii)

2.96 m/sec
(iii)

1.96 m/sec
(iv)

8.96 m/sec
(v)

0.96 m/sec

Question 9

9.

A man 1.9 m tall stands at a distance of 7.9 m from a lamp post and casts a shadow of 3.5 m on the ground. Find the height of the lamp post .

(i)

7.19 m
(ii)

4.19 m
(iii)

8.19 m
(iv)

6.19 m
(v)

5.19 m

Question 10

10.

Two vertical poles are on either side of a road. A 33 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 30° 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)

54.91 m
(ii)

46.91 m
(iii)

56.91 m
(iv)

48.91 m
(v)

51.91 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)

∠c
(ii)

∠d
(iii)

∠e
(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)

∠e
(iii)

∠g
(iv)

∠d

Assignment Key