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
60°
.
If the height of the
chimney
is
40 m
,
find the distance between
the observation point and the top of the
chimney
.

(i)

80

m
(ii)

80
3

√

3

m
(iii)

80
3

√

18

m
(iv)

80
3

m
(v)

40

√

2

m

Question 2

2.

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
90 m
,
find the distance between
the observation point and the foot of the
chimney
.

(i)

89

m
(ii)

93

m
(iii)

88

m
(iv)

90

m
(v)

91

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
60°
.
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)

139

m
(ii)

141

m
(iii)

140

m
(iv)

142

m
(v)

138

m

Question 4

4.

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

(i)

180

m
(ii)

60

m
(iii)

60

√

3

m
(iv)

60

√

18

m
(v)

90

√

2

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
10 m
,
find the height of the
radio tower
.

(i)

2

m
(ii)

4

m
(iii)

5

m
(iv)

7

m
(v)

6

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
30°
.
If the distance between the point and the top of the
tower
is
110 m
,
find the distance between
the observation point and the foot of the
tower
.

(i)

55

m
(ii)

55

√

18

m
(iii)

55

√

3

m
(iv)

165

m
(v)

165
2

√

2

m

Question 7

7.

Two boys are on opposite sides of a tower of 160 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)

(

160

+

160
3

√

3

)

m
(ii)

(

2

+

√

3

)

m
(iii)

(

80

√

6

+

80

√

2

)

m
(iv)

51200
3

m
(v)

(

160

√

6

+

160
3

√

18

)

m

Question 8

8.

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)

(

5

√

3

+

5

)

m
(ii)

(

2

+

√

3

)

m
(iii)

(

15
2

√

2

+

5
2

√

6

)

m
(iv)

(

5

√

18

+

5

√

6

)

m
(v)

50

m

Question 9

9.

A flagstaff stands on the top of a building at a distance of 10 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 45°. Find the height of the flagstaff .

(i)

(

10

√

18

−

10

√

6

)

m
(ii)

(

15

√

2

−

5

√

6

)

m
(iii)

200

m
(iv)

(

2

−

√

3

)

m
(v)

(

10

√

3

−

10

)

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
4

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

(i)

98.00 m
(ii)

120.00 m
(iii)

127.00 m
(iv)

132.00 m
(v)

103.00 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)

(

1
2

)
.
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)

43.00 m
(ii)

40.00 m
(iii)

37.00 m
(iv)

45.00 m
(v)

35.00 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)

(

5
7

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

(i)

147.71 m
(ii)

135.71 m
(iii)

109.71 m
(iv)

129.71 m
(v)

142.71 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)

(

4
3

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

(i)

62.50 m
(ii)

72.50 m
(iii)

67.50 m
(iv)

64.50 m
(v)

70.50 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)

(

3
2

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

(i)

302.00 m
(ii)

293.00 m
(iii)

280.00 m
(iv)

272.00 m
(v)

285.00 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)

(

1
2

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

(i)

83.00 m
(ii)

100.00 m
(iii)

86.00 m
(iv)

118.00 m
(v)

116.00 m

Question 16

16.

A
tower
stands vertically on the ground.

The height of the
tower
is
110

√

3

m
.

The distance between the observation point and its top
is
220

m
.

Find the angle of elevation.

(i)

45°
(ii)

60°
(iii)

105°
(iv)

90°
(v)

30°

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 100 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

223.42 m
(ii)

267.42 m
(iii)

258.42 m
(iv)

241.42 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 150 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 width of the river .

(i)

174.00 m
(ii)

146.00 m
(iii)

150.00 m
(iv)

133.00 m
(v)

167.00 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 10 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)

5.67 m
(ii)

7.67 m
(iii)

8.67 m
(iv)

6.67 m
(v)

4.67 m

Question 20

20.

An observer 1.4 m tall, is 130 m away from a tower . The angle of elevation of the top of the tower from her eyes is 60°. Find the height of the tower .

(i)

243.57 m
(ii)

218.57 m
(iii)

232.57 m
(iv)

226.57 m
(v)

199.57 m

Question 21

21.

Two poles of equal height are standing opposite to each other on either side of a road which is 35 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 =

23.19 m

, distances away =

13.81 m

,

23.19 m
(ii)
height =

20.19 m

, distances away =

10.81 m

,

20.19 m
(iii)
height =

24.19 m

, distances away =

14.81 m

,

24.19 m
(iv)
height =

21.19 m

, distances away =

11.81 m

,

21.19 m
(v)
height =

22.19 m

, distances away =

12.81 m

,

22.19 m

Question 22

22.

From the top of a light house which is 45 m high from the sea level, the angles of depression of two ships are 60° 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)

46.96 m
(ii)

56.96 m
(iii)

48.96 m
(iv)

51.96 m
(v)

54.96 m

Question 23

23.

From the top of a 18 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)

52.17 m
(ii)

54.17 m
(iii)

49.17 m
(iv)

46.17 m
(v)

44.17 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 65 m, find the height of the building .

(i)

135.59 m
(ii)

108.59 m
(iii)

112.59 m
(iv)

99.59 m
(v)

114.59 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 60° and the angle of elevation of the top of the building is 30°. If the height of the building is 17 m, find the height of the flag staff .

(i)

37.00 m
(ii)

34.00 m
(iii)

39.00 m
(iv)

31.00 m
(v)

29.00 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 15 m, find the height of the building .

(i)

9.50 m
(ii)

8.50 m
(iii)

6.50 m
(iv)

5.50 m
(v)

7.50 m

Assignment Key