EduSahara™ Worksheet

Question 1

1.

Two boys are on opposite sides of a tower of 70 m height. They measure the angle of elevation of the top of the tower as 60° and 30° respectively. Find the distance between the two boys.

(i)

280
3

m
(ii)

280

m
(iii)

140

√

2

m
(iv)

280
3

√

3

m
(v)

280
3

√

18

m

Question 2

2.

A person, walking 35 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 45°. Find the height of the flagpost .

(i)

(

2

+

√

3

)

m
(ii)

(

35
2

√

18

+

35
2

√

6

)

m
(iii)

(

35
2

√

3

+

35
2

)

m
(iv)

(

105
4

√

2

+

35
4

√

6

)

m
(v)

1225
2

m

Question 3

3.

A flagstaff stands on the top of a building at a distance of 25 m away from the foot of building . The angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 30°. Find the height of the flagstaff .

(i)

50
3

√

18

m
(ii)

50

m
(iii)

25

√

2

m
(iv)

50
3

m
(v)

50
3

√

3

m

Question 4

4.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 50 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 60° respectively. Find the width of the river .

(i)

33.87 m
(ii)

23.87 m
(iii)

31.87 m
(iv)

28.87 m
(v)

25.87 m

Question 5

5.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 110 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 60° respectively. Find the height of the other temple.

(i)

68.33 m
(ii)

76.33 m
(iii)

70.33 m
(iv)

78.33 m
(v)

73.33 m

Question 6

6.

Two poles of equal height are standing opposite to each other on either side of a road which is 20 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 45° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

14.68 m

, distances away =

14.68 m

,

9.32 m
(ii)
height =

11.68 m

, distances away =

11.68 m

,

6.32 m
(iii)
height =

10.68 m

, distances away =

10.68 m

,

5.32 m
(iv)
height =

12.68 m

, distances away =

12.68 m

,

7.32 m
(v)
height =

13.68 m

, distances away =

13.68 m

,

8.32 m

Question 7

7.

From the top of a light house which is 25 m high from the sea level, the angles of depression of two ships are 60° and 45°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.

(i)

15.57 m
(ii)

7.57 m
(iii)

13.57 m
(iv)

10.57 m
(v)

5.57 m

Question 8

8.

From the top of a 15 m high building , the angle of elevation of the top of a cable tower is 45° and the angle of depression of its foot is 30°. Find the height of the cable tower.

(i)

43.98 m
(ii)

37.98 m
(iii)

35.98 m
(iv)

40.98 m
(v)

45.98 m

Question 9

9.

The angle of elevation of the top of a building from the foot of a tower is 60°. The angle of elevation of the top of the tower from the foot of the building is 30°. If the height of the tower is 65 m, find the height of the building .

(i)

211.99 m
(ii)

220.99 m
(iii)

194.99 m
(iv)

166.99 m
(v)

187.99 m

Question 10

10.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 45°. If the height of the building is 16 m, find the height of the flag staff .

(i)

8.71 m
(ii)

11.71 m
(iii)

6.71 m
(iv)

14.71 m
(v)

16.71 m

Question 11

11.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 6 m, find the height of the building .

(i)

5.00 m
(ii)

4.00 m
(iii)

2.00 m
(iv)

1.00 m
(v)

3.00 m

Question 12

12.

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 60° and 30° respectively. Find the height of the cliff.

(i)

93.16 m
(ii)

95.16 m
(iii)

98.16 m
(iv)

103.16 m
(v)

101.16 m

Question 13

13.

From a point 160 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)

172.75 m
(ii)

186.75 m
(iii)

201.75 m
(iv)

184.75 m
(v)

158.75 m

Question 14

14.

The angles of depression of two boats from the top of a cliff 100 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

70.21 m
(ii)

73.21 m
(iii)

78.21 m
(iv)

68.21 m
(v)

76.21 m

Question 15

15.

The angles of depression of two boats from the top of a cliff 190 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)

297.71 m
(ii)

306.71 m
(iii)

312.71 m
(iv)

299.71 m
(v)

285.71 m

Question 16

16.

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)

12 min 37 sec
(ii)

10 min 35 sec
(iii)

8 min 33 sec
(iv)

6 min 32 sec
(v)

9 min 34 sec

Question 17

17.

The shadow of a vertical tower BA on a level ground is increased by 20 m, when the altitude of the sun changes from 60° to 45°. Find the height of the tower .

(i)

42.32 m
(ii)

47.32 m
(iii)

44.32 m
(iv)

50.32 m
(v)

52.32 m

Question 18

18.

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 60° and 45° and the distance between them is 170 m , find the height of the cliff.

(i)

130.78 m
(ii)

105.78 m
(iii)

85.78 m
(iv)

121.78 m
(v)

107.78 m

Question 19

19.

A man in a boat rowing away from a lighthouse 40 m high, takes 4 min to change the angle of elevation of the top of the lighthouse from 45° to 30°. Find the speed of the boat.

(i)

2.12 m/sec
(ii)

8.12 m/sec
(iii)

1.12 m/sec
(iv)

0.12 m/sec
(v)

7.12 m/sec

Question 20

20.

Two vertical poles are on either side of a road. A 30 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 60° with the road. Find the width of the road.

(i)

45.98 m
(ii)

43.98 m
(iii)

37.98 m
(iv)

35.98 m
(v)

40.98 m

Assignment Key