EduSahara™ Worksheet

Question 1

1.

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 45° respectively. Find the height of the cliff.

(i)

85.00 m
(ii)

90.00 m
(iii)

93.00 m
(iv)

87.00 m
(v)

95.00 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 45° and 30° respectively. Find the height of the pillar.

(i)

80.29 m
(ii)

75.29 m
(iii)

85.29 m
(iv)

83.29 m
(v)

77.29 m

Question 3

3.

The angles of depression of two boats from the top of a cliff 80 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)

95.38 m
(ii)

89.38 m
(iii)

97.38 m
(iv)

92.38 m
(v)

87.38 m

Question 4

4.

The angles of depression of two boats from the top of a cliff 70 m high are 60° and 45° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

135.42 m
(ii)

106.42 m
(iii)

86.42 m
(iv)

128.42 m
(v)

110.42 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 30° to 60°, how soon after this, will the car reach the observation tower?

(i)

5 min 32 sec
(ii)

2 min 29 sec
(iii)

1 min 27 sec
(iv)

4 min 31 sec
(v)

3 min 30 sec

Question 6

6.

The shadow of a vertical tower BA on a level ground is increased by 35 m, when the altitude of the sun changes from 60° to 45°. Find the height of the tower .

(i)

87.81 m
(ii)

77.81 m
(iii)

82.81 m
(iv)

79.81 m
(v)

85.81 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 30° and 45° and the distance between them is 140 m , find the height of the cliff.

(i)

51.25 m
(ii)

54.25 m
(iii)

46.25 m
(iv)

56.25 m
(v)

48.25 m

Question 8

8.

A man in a boat rowing away from a lighthouse 95 m high, takes 2 min to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat.

(i)

7.91 m/sec
(ii)

1.91 m/sec
(iii)

2.91 m/sec
(iv)

0.91 m/sec
(v)

8.91 m/sec

Question 9

9.

A man 1.5 m tall stands at a distance of 3.7 m from a lamp post and casts a shadow of 4.8 m on the ground. Find the height of the lamp post .

(i)

2.66 m
(ii)

3.66 m
(iii)

4.66 m
(iv)

1.66 m
(v)

0.66 m

Question 10

10.

Two vertical poles are on either side of a road. A 26 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)

31.38 m
(ii)

28.38 m
(iii)

26.38 m
(iv)

36.38 m
(v)

34.38 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)

∠b
(iii)

∠a
(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)

∠b
(ii)

∠d
(iii)

∠c
(iv)

∠e

Assignment Key