EduSahara™ Worksheet

Question 1

1.

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

(i)

121

m
(ii)

119

m
(iii)

120

m
(iv)

118

m
(v)

123

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
50 m
,
find the distance between
the observation point and the foot of the
radio tower
.

(i)

50
3

√

18

m
(ii)

50

m
(iii)

50
3

m
(iv)

25

√

2

m
(v)

50
3

√

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

(i)

237

m
(ii)

242

m
(iii)

241

m
(iv)

240

m
(v)

239

m

Question 4

4.

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

(i)

45

√

2

m
(ii)

30

√

3

m
(iii)

30

m
(iv)

90

m
(v)

30

√

18

m

Question 5

5.

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

(i)

5

√

3

m
(ii)

5

√

18

m
(iii)

15

m
(iv)

5

m
(v)

15
2

√

2

m

Question 6

6.

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 top of the
chimney
is
180 m
,
find the distance between
the observation point and the foot of the
chimney
.

(i)

90

m
(ii)

92

m
(iii)

89

m
(iv)

91

m
(v)

87

m

Question 7

7.

Two boys are on opposite sides of a tower of 30 m height. They measure the angle of elevation of the top of the tower as 60° and 45° respectively. Find the distance between the two boys.

(i)

(

−

600

)

m
(ii)

(

10

√

3

+

30

)

m
(iii)

(

−

2

−

√

3

)

m
(iv)

(

10

√

18

+

30

√

6

)

m
(v)

(

15

√

2

+

15

√

6

)

m

Question 8

8.

A person, walking 10 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)

150

m
(ii)

(

15
2

√

6

+

15
2

√

2

)

m
(iii)

(

15

√

6

+

5

√

18

)

m
(iv)

(

15

+

5

√

3

)

m
(v)

(

2

+

√

3

)

m

Question 9

9.

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

√

3

m
(ii)

50
3

m
(iii)

50
3

√

18

m
(iv)

25

√

2

m
(v)

50

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)

(

2
3

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

(i)

48.33 m
(ii)

53.33 m
(iii)

56.33 m
(iv)

50.33 m
(v)

58.33 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)

(

3
8

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

(i)

269.33 m
(ii)

310.33 m
(iii)

275.33 m
(iv)

311.33 m
(v)

293.33 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 height of the
tower
is
130 m
,
find the distance between
the observation point and the foot of the
tower
.

(i)

244.00 m
(ii)

260.00 m
(iii)

245.00 m
(iv)

277.00 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)

(

8
5

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

(i)

61.25 m
(ii)

56.25 m
(iii)

53.25 m
(iv)

59.25 m
(v)

51.25 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)

(

11
9

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

(i)

217.00 m
(ii)

238.00 m
(iii)

197.00 m
(iv)

220.00 m
(v)

235.00 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
3

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

(i)

63.33 m
(ii)

68.33 m
(iii)

60.33 m
(iv)

66.33 m
(v)

58.33 m

Question 16

16.

A
tower
stands vertically on the ground.

The height of the
tower
is
190

√

2

m
.

The distance between the observation point and its top
is
380

m
.

Find the angle of elevation.

(i)

30°
(ii)

105°
(iii)

45°
(iv)

60°
(v)

75°

Question 17

17.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 30° with the ground. The top of the tree touches the ground at a distance of 50 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

86.61 m
(ii)

81.61 m
(iii)

83.61 m
(iv)

91.61 m
(v)

89.61 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 70 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)

37.41 m
(ii)

40.41 m
(iii)

45.41 m
(iv)

35.41 m
(v)

43.41 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)

7.67 m
(ii)

5.67 m
(iii)

4.67 m
(iv)

6.67 m
(v)

8.67 m

Question 20

20.

An observer 1.6 m tall, is 110 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)

124.60 m
(ii)

95.60 m
(iii)

126.60 m
(iv)

111.60 m
(v)

94.60 m

Question 21

21.

Two poles of equal height are standing opposite to each other on either side of a road which is 15 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30° and 60° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

8.5 m

, distances away =

5.75 m

,

13.25 m
(ii)
height =

7.5 m

, distances away =

4.75 m

,

12.25 m
(iii)
height =

5.5 m

, distances away =

2.75 m

,

10.25 m
(iv)
height =

4.5 m

, distances away =

1.75 m

,

9.25 m
(v)
height =

6.5 m

, distances away =

3.75 m

,

11.25 m

Question 22

22.

From the top of a light house which is 85 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)

38.93 m
(ii)

35.93 m
(iii)

32.93 m
(iv)

30.93 m
(v)

40.93 m

Question 23

23.

From the top of a 19 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Find the height of the cable tower.

(i)

73.00 m
(ii)

81.00 m
(iii)

76.00 m
(iv)

71.00 m
(v)

79.00 m

Question 24

24.

The angle of elevation of the top of a building from the foot of a tower is 45°. 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 30 m, find the height of the building .

(i)

51.96 m
(ii)

46.96 m
(iii)

56.96 m
(iv)

54.96 m
(v)

48.96 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 60° and the angle of elevation of the top of the building is 45°. If the height of the building is 20 m, find the height of the flag staff .

(i)

17.64 m
(ii)

19.64 m
(iii)

11.64 m
(iv)

9.64 m
(v)

14.64 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 45° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 19 m, find the height of the building .

(i)

28.96 m
(ii)

30.96 m
(iii)

22.96 m
(iv)

25.96 m
(v)

20.96 m

Assignment Key