EduSahara™ Worksheet

Question 1

1.

From a point 170 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)

103.16 m
(ii)

98.16 m
(iii)

101.16 m
(iv)

95.16 m
(v)

93.16 m

Question 2

2.

From a point 70 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)

26.58 m
(ii)

24.58 m
(iii)

34.58 m
(iv)

29.58 m
(v)

32.58 m

Question 3

3.

The angles of depression of two boats from the top of a cliff 90 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)

65.89 m
(ii)

60.89 m
(iii)

62.89 m
(iv)

70.89 m
(v)

68.89 m

Question 4

4.

The angles of depression of two boats from the top of a cliff 140 m high are 45° and 60° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

220.84 m
(ii)

207.84 m
(iii)

242.84 m
(iv)

236.84 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 45° to 60°, how soon after this, will the car reach the observation tower?

(i)

16 min 10 sec
(ii)

19 min 7 sec
(iii)

18 min 11 sec
(iv)

21 min 15 sec
(v)

20 min 13 sec

Question 6

6.

The shadow of a vertical tower BA on a level ground is increased by 45 m, when the altitude of the sun changes from 60° to 30°. Find the height of the tower .

(i)

33.98 m
(ii)

38.98 m
(iii)

35.98 m
(iv)

43.98 m
(v)

41.98 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 225 m , find the height of the cliff.

(i)

79.36 m
(ii)

82.36 m
(iii)

87.36 m
(iv)

77.36 m
(v)

85.36 m

Question 8

8.

A man in a boat rowing away from a lighthouse 55 m high, takes 2.5 min to change the angle of elevation of the top of the lighthouse from 45° to 30°. Find the speed of the boat.

(i)

8.27 m/sec
(ii)

2.27 m/sec
(iii)

1.27 m/sec
(iv)

7.27 m/sec
(v)

0.27 m/sec

Question 9

9.

A man 1.6 m tall stands at a distance of 7.2 m from a lamp post and casts a shadow of 4.6 m on the ground. Find the height of the lamp post .

(i)

3.10 m
(ii)

5.10 m
(iii)

4.10 m
(iv)

6.10 m
(v)

2.10 m

Question 10

10.

Two vertical poles are on either side of a road. A 35 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)

47.25 m
(ii)

39.25 m
(iii)

37.25 m
(iv)

45.25 m
(v)

42.25 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)

∠e
(iii)

∠d
(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)

∠e
(ii)

∠c
(iii)

∠d
(iv)

∠b

Assignment Key