EduSahara™ Worksheet

Question 1

1.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
45°
.
If the height of the
chimney
is
80 m
,
find the distance between
the observation point and the top of the
chimney
.

(i)

160

m
(ii)

160

√

3

m
(iii)

40

√

12

m
(iv)

80

m
(v)

80

√

2

m

Question 2

2.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
60°
.
If the height of the
radio tower
is
30 m
,
find the distance between
the observation point and the foot of the
radio tower
.

(i)

30

m
(ii)

15

√

2

m
(iii)

10

m
(iv)

10

√

18

m
(v)

10

√

3

m

Question 3

3.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
30°
.
If the distance between the point and the foot of the
chimney
is
70 m
,
find the distance between
the observation point and the top of the
chimney
.

(i)

140
3

√

18

m
(ii)

140
3

m
(iii)

140
3

√

3

m
(iv)

70

√

2

m
(v)

140

m

Question 4

4.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
60°
.
If the distance between the point and the foot of the
tower
is
150 m
,
find the height of the
tower
.

(i)

225

√

2

m
(ii)

450

m
(iii)

150

m
(iv)

150

√

18

m
(v)

150

√

3

m

Question 5

5.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
30°
.
If the distance between the point and the top of the
radio tower
is
140 m
,
find the height of the
radio tower
.

(i)

71

m
(ii)

70

m
(iii)

73

m
(iv)

69

m
(v)

67

m

Question 6

6.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
60°
.
If the distance between the point and the top of the
tower
is
30 m
,
find the distance between
the observation point and the foot of the
tower
.

(i)

15

m
(ii)

14

m
(iii)

13

m
(iv)

18

m
(v)

16

m

Question 7

7.

Two boys are on opposite sides of a tower of 150 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)

200

√

3

m
(ii)

300

√

2

m
(iii)

600

m
(iv)

200

√

18

m
(v)

200

m

Question 8

8.

A person, walking 40 m from a point toward a flagpost , observes that its angle of elevation changes from 45° to 60°. Find the height of the flagpost .

(i)

2400

m
(ii)

(

30

√

6

+

30

√

2

)

m
(iii)

(

60

√

6

+

20

√

18

)

m
(iv)

(

2

+

√

3

)

m
(v)

(

60

+

20

√

3

)

m

Question 9

9.

A flagstaff stands on the top of a building at a distance of 50 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)

100

m
(ii)

100
3

√

3

m
(iii)

100
3

m
(iv)

50

√

2

m
(v)

100
3

√

18

m

Question 10

10.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
sin

(-1)

(

1
8

)
.
If the distance between the point and the top of the
tower
is
200 m
,
find the height of the
tower
.

(i)

20.00 m
(ii)

22.00 m
(iii)

25.00 m
(iv)

28.00 m
(v)

30.00 m

Question 11

11.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
cos

(-1)

(

5
7

)
.
If the distance between the point and the top of the
tower
is
150 m
,
find the distance between
the observation point and the foot of the
tower
.

(i)

112.14 m
(ii)

100.14 m
(iii)

131.14 m
(iv)

107.14 m
(v)

89.14 m

Question 12

12.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
tan

(-1)

(

1
2

)
.
If the distance between the point and the foot of the
tower
is
60 m
,
find the height of the
tower
.

(i)

27.00 m
(ii)

25.00 m
(iii)

33.00 m
(iv)

35.00 m
(v)

30.00 m

Question 13

13.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
cosec

(-1)

(

9
7

)
.
If the height of the
tower
is
120 m
,
find the distance between
the observation point and the top of the
tower
.

(i)

172.29 m
(ii)

177.29 m
(iii)

127.29 m
(iv)

148.29 m
(v)

154.29 m

Question 14

14.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
sec

(-1)

(

4
3

)
.
If the distance between the point and the foot of the
tower
is
20 m
,
find the distance between
the observation point and the top of the
tower
.

(i)

23.67 m
(ii)

26.67 m
(iii)

29.67 m
(iv)

21.67 m
(v)

31.67 m

Question 15

15.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
cot

(-1)

(

8
9

)
.
If the distance between the point and the foot of the
tower
is
180 m
,
find the height of the
tower
.

(i)

177.50 m
(ii)

196.50 m
(iii)

202.50 m
(iv)

214.50 m
(v)

218.50 m

Question 16

16.

A
tower
stands vertically on the ground.

The height of the
tower
is
50

m
.

The distance between the observation point and its foot
is
50

m
.

Find the angle of elevation.

(i)

75°
(ii)

30°
(iii)

45°
(iv)

60°
(v)

105°

Question 17

17.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 45° with the ground. The top of the tree touches the ground at a distance of 20 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

51.28 m
(ii)

43.28 m
(iii)

48.28 m
(iv)

53.28 m
(v)

45.28 m

Question 18

18.

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 45° and 60° respectively. Find the width of the river .

(i)

63.51 m
(ii)

68.51 m
(iii)

66.51 m
(iv)

58.51 m
(v)

60.51 m

Question 19

19.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 160 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 45° and 60° respectively. Find the height of the other temple.

(i)

64.63 m
(ii)

67.63 m
(iii)

72.63 m
(iv)

70.63 m
(v)

62.63 m

Question 20

20.

An observer 1.3 m tall, is 100 m away from a tower . The angle of elevation of the top of the tower from her eyes is 45°. Find the height of the tower .

(i)

87.30 m
(ii)

116.30 m
(iii)

119.30 m
(iv)

88.30 m
(v)

101.30 m

Question 21

21.

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 45° and 60° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

27.53 m

, distances away =

15.47 m

,

27.53 m
(ii)
height =

28.53 m

, distances away =

16.47 m

,

28.53 m
(iii)
height =

26.53 m

, distances away =

14.47 m

,

26.53 m
(iv)
height =

30.53 m

, distances away =

18.47 m

,

30.53 m
(v)
height =

29.53 m

, distances away =

17.47 m

,

29.53 m

Question 22

22.

From the top of a light house which is 100 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)

42.27 m
(ii)

39.27 m
(iii)

45.27 m
(iv)

37.27 m
(v)

47.27 m

Question 23

23.

From the top of a 10 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)

24.32 m
(ii)

30.32 m
(iii)

32.32 m
(iv)

22.32 m
(v)

27.32 m

Question 24

24.

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 45°. If the height of the tower is 30 m, find the height of the building .

(i)

48.96 m
(ii)

56.96 m
(iii)

54.96 m
(iv)

51.96 m
(v)

46.96 m

Question 25

25.

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 building is 16 m, find the height of the flag staff .

(i)

8.71 m
(ii)

14.71 m
(iii)

16.71 m
(iv)

11.71 m
(v)

6.71 m

Question 26

26.

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 8 m, find the height of the building .

(i)

6.00 m
(ii)

5.00 m
(iii)

3.00 m
(iv)

4.00 m
(v)

2.00 m

Assignment Key