EduSahara™ Worksheet

Question 1

1.

From a point 80 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)

85.00 m
(ii)

75.00 m
(iii)

80.00 m
(iv)

83.00 m
(v)

77.00 m

Question 2

2.

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

(i)

151.10 m
(ii)

132.10 m
(iii)

139.10 m
(iv)

115.10 m
(v)

142.10 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)

191.85 m
(ii)

180.85 m
(iii)

213.85 m
(iv)

207.85 m
(v)

232.85 m

Question 4

4.

The angles of depression of two boats from the top of a cliff 70 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)

149.67 m
(ii)

175.67 m
(iii)

161.67 m
(iv)

174.67 m
(v)

144.67 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 7 min for the angle of depression to change from 45° to 60°, how soon after this, will the car reach the observation tower?

(i)

7 min 31 sec
(ii)

10 min 35 sec
(iii)

9 min 34 sec
(iv)

12 min 36 sec
(v)

8 min 33 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 60° to 30°. Find the height of the tower .

(i)

22.98 m
(ii)

20.98 m
(iii)

25.98 m
(iv)

28.98 m
(v)

30.98 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 30° and the distance between them is 190 m , find the height of the cliff.

(i)

66.55 m
(ii)

69.55 m
(iii)

72.55 m
(iv)

74.55 m
(v)

64.55 m

Question 8

8.

A man in a boat rowing away from a lighthouse 80 m high, takes 5 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.

(i)

8.11 m/sec
(ii)

2.11 m/sec
(iii)

0.11 m/sec
(iv)

7.11 m/sec
(v)

1.11 m/sec

Question 9

9.

A man 1.7 m tall stands at a distance of 4.7 m from a lamp post and casts a shadow of 5.3 m on the ground. Find the height of the lamp post .

(i)

4.21 m
(ii)

2.21 m
(iii)

5.21 m
(iv)

1.21 m
(v)

3.21 m

Question 10

10.

Two vertical poles are on either side of a road. A 36 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)

56.63 m
(ii)

59.63 m
(iii)

61.63 m
(iv)

51.63 m
(v)

53.63 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)

∠c
(iii)

∠e
(iv)

∠b

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)

∠a
(iv)

∠b

Assignment Key