EduSahara™ Worksheet

Question 1

1.

From a point 190 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)

122.71 m
(ii)

81.71 m
(iii)

95.71 m
(iv)

127.71 m
(v)

109.71 m

Question 2

2.

From a point 130 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)

133.11 m
(ii)

162.11 m
(iii)

166.11 m
(iv)

150.11 m
(v)

147.11 m

Question 3

3.

The angles of depression of two boats from the top of a cliff 170 m high are 30° and 45° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

111.46 m
(ii)

96.46 m
(iii)

148.46 m
(iv)

124.46 m
(v)

129.46 m

Question 4

4.

The angles of depression of two boats from the top of a cliff 110 m high are 30° and 60° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

226.05 m
(ii)

267.05 m
(iii)

242.05 m
(iv)

270.05 m
(v)

254.05 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 60°, how soon after this, will the car reach the observation tower?

(i)

6 min 4 sec
(ii)

7 min 0 sec
(iii)

5 min 2 sec
(iv)

8 min 6 sec
(v)

9 min 7 sec

Question 6

6.

The shadow of a vertical tower BA on a level ground is increased by 30 m, when the altitude of the sun changes from 45° to 30°. Find the height of the tower .

(i)

45.99 m
(ii)

35.99 m
(iii)

43.99 m
(iv)

40.99 m
(v)

37.99 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 140 m , find the height of the cliff.

(i)

83.76 m
(ii)

93.76 m
(iii)

88.76 m
(iv)

85.76 m
(v)

91.76 m

Question 8

8.

A man in a boat rowing away from a lighthouse 90 m high, takes 2 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.

(i)

7.32 m/sec
(ii)

1.32 m/sec
(iii)

8.32 m/sec
(iv)

2.32 m/sec
(v)

0.32 m/sec

Question 9

9.

A man 1.3 m tall stands at a distance of 2.1 m from a lamp post and casts a shadow of 5.8 m on the ground. Find the height of the lamp post .

(i)

9.77 m
(ii)

0.77 m
(iii)

2.77 m
(iv)

3.77 m
(v)

1.77 m

Question 10

10.

Two vertical poles are on either side of a road. A 31 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 30° with the road. Find the width of the road.

(i)

39.35 m
(ii)

45.35 m
(iii)

37.35 m
(iv)

47.35 m
(v)

42.35 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)

∠d
(ii)

∠f
(iii)

∠c
(iv)

∠e

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)

∠c
(ii)

∠d
(iii)

∠e
(iv)

∠f

Assignment Key