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 45° and 60° respectively. Find the distance between the two boys.

(i)

(

70

√

6

+

70
3

√

18

)

m
(ii)

(

2

+

√

3

)

m
(iii)

(

35

√

6

+

35

√

2

)

m
(iv)

(

70

+

70
3

√

3

)

m
(v)

9800
3

m

Question 2

2.

A person, walking 10 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)

(

5

√

3

+

5

)

m
(iii)

50

m
(iv)

(

15
2

√

2

+

5
2

√

6

)

m
(v)

(

5

√

18

+

5

√

6

)

m

Question 3

3.

A flagstaff stands on the top of a building at a distance of 45 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)

30

√

3

m
(ii)

30

m
(iii)

30

√

18

m
(iv)

45

√

2

m
(v)

90

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 90 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)

56.96 m
(ii)

48.96 m
(iii)

51.96 m
(iv)

46.96 m
(v)

54.96 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 190 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 45° respectively. Find the height of the other temple.

(i)

83.29 m
(ii)

77.29 m
(iii)

85.29 m
(iv)

75.29 m
(v)

80.29 m

Question 6

6.

Two poles of equal height are standing opposite to each other on either side of a road which is 45 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

19.49 m

, distances away =

33.75 m

,

11.25 m
(ii)
height =

17.49 m

, distances away =

31.75 m

,

9.25 m
(iii)
height =

20.49 m

, distances away =

34.75 m

,

12.25 m
(iv)
height =

21.49 m

, distances away =

35.75 m

,

13.25 m
(v)
height =

18.49 m

, distances away =

32.75 m

,

10.25 m

Question 7

7.

From the top of a light house which is 55 m high from the sea level, the angles of depression of two ships are 45° and 30°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.

(i)

37.25 m
(ii)

45.25 m
(iii)

35.25 m
(iv)

40.25 m
(v)

43.25 m

Question 8

8.

From the top of a 20 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)

59.64 m
(ii)

49.64 m
(iii)

57.64 m
(iv)

51.64 m
(v)

54.64 m

Question 9

9.

The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 85 m, find the height of the building .

(i)

28.33 m
(ii)

33.33 m
(iii)

31.33 m
(iv)

23.33 m
(v)

25.33 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 30°. If the height of the building is 10 m, find the height of the flag staff .

(i)

15.00 m
(ii)

20.00 m
(iii)

25.00 m
(iv)

17.00 m
(v)

23.00 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 45° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 13 m, find the height of the building .

(i)

20.76 m
(ii)

22.76 m
(iii)

17.76 m
(iv)

12.76 m
(v)

14.76 m

Question 12

12.

From a point 60 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)

55.00 m
(ii)

60.00 m
(iii)

65.00 m
(iv)

63.00 m
(v)

57.00 m

Question 13

13.

From a point 110 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)

49.49 m
(ii)

43.49 m
(iii)

46.49 m
(iv)

41.49 m
(v)

51.49 m

Question 14

14.

The angles of depression of two boats from the top of a cliff 130 m high are 60° and 45° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

54.94 m
(ii)

49.94 m
(iii)

59.94 m
(iv)

57.94 m
(v)

51.94 m

Question 15

15.

The angles of depression of two boats from the top of a cliff 110 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

317.53 m
(ii)

284.53 m
(iii)

316.53 m
(iv)

275.53 m
(v)

300.53 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 17 min for the angle of depression to change from 45° to 60°, how soon after this, will the car reach the observation tower?

(i)

23 min 13 sec
(ii)

24 min 14 sec
(iii)

22 min 12 sec
(iv)

20 min 10 sec
(v)

26 min 16 sec

Question 17

17.

The shadow of a vertical tower BA on a level ground is increased by 5 m, when the altitude of the sun changes from 60° to 30°. Find the height of the tower .

(i)

6.33 m
(ii)

4.33 m
(iii)

5.33 m
(iv)

2.33 m
(v)

3.33 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 45° and 30° and the distance between them is 160 m , find the height of the cliff.

(i)

53.57 m
(ii)

61.57 m
(iii)

63.57 m
(iv)

55.57 m
(v)

58.57 m

Question 19

19.

A man in a boat rowing away from a lighthouse 35 m high, takes 1.5 min to change the angle of elevation of the top of the lighthouse from 45° to 30°. Find the speed of the boat.

(i)

1.28 m/sec
(ii)

7.28 m/sec
(iii)

8.28 m/sec
(iv)

0.28 m/sec
(v)

2.28 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 45° with the pole and when it is turned to rest against another pole, it makes an angle of 30° with the road. Find the width of the road.

(i)

50.19 m
(ii)

47.19 m
(iii)

44.19 m
(iv)

52.19 m
(v)

42.19 m

Assignment Key