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

(i)

173.00 m
(ii)

194.00 m
(iii)

185.00 m
(iv)

190.00 m
(v)

214.00 m

Question 2

2.

From a point 120 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)

84.85 m
(ii)

87.85 m
(iii)

82.85 m
(iv)

92.85 m
(v)

90.85 m

Question 3

3.

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 same side of the cliff .

(i)

100.17 m
(ii)

90.17 m
(iii)

92.17 m
(iv)

98.17 m
(v)

95.17 m

Question 4

4.

The angles of depression of two boats from the top of a cliff 100 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)

270.21 m
(ii)

273.21 m
(iii)

278.21 m
(iv)

285.21 m
(v)

256.21 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 9 min for the angle of depression to change from 30° to 60°, how soon after this, will the car reach the observation tower?

(i)

3 min 29 sec
(ii)

5 min 31 sec
(iii)

6 min 33 sec
(iv)

4 min 30 sec
(v)

2 min 28 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 45°. Find the height of the tower .

(i)

30.49 m
(ii)

38.49 m
(iii)

32.49 m
(iv)

40.49 m
(v)

35.49 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 60° and the distance between them is 140 m , find the height of the cliff.

(i)

63.63 m
(ii)

57.63 m
(iii)

60.63 m
(iv)

65.63 m
(v)

55.63 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)

1.11 m/sec
(iii)

2.11 m/sec
(iv)

7.11 m/sec
(v)

0.11 m/sec

Question 9

9.

A man 1.5 m tall stands at a distance of 1.4 m from a lamp post and casts a shadow of 3.7 m on the ground. Find the height of the lamp post .

(i)

1.07 m
(ii)

2.07 m
(iii)

4.07 m
(iv)

0.07 m
(v)

3.07 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 45° with the pole and when it is turned to rest against another pole, it makes an angle of 60° with the road. Find the width of the road.

(i)

39.83 m
(ii)

42.83 m
(iii)

34.83 m
(iv)

44.83 m
(v)

36.83 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)

∠a
(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)

∠d
(ii)

∠e
(iii)

∠c
(iv)

∠b

Assignment Key