EduSahara™ Worksheet

Question 1

1.

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

(i)

160

m
(ii)

162

m
(iii)

161

m
(iv)

159

m
(v)

157

m

Question 2

2.

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

(i)

110

√

3

m
(ii)

165

√

2

m
(iii)

110

√

18

m
(iv)

110

m
(v)

330

m

Question 3

3.

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

(i)

40
3

√

18

m
(ii)

20

√

2

m
(iii)

40
3

√

3

m
(iv)

40

m
(v)

40
3

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
70 m
,
find the height of the
radio tower
.

(i)

210

m
(ii)

105

√

2

m
(iii)

70

√

18

m
(iv)

70

m
(v)

70

√

3

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
45°
.
If the distance between the point and the top of the
building
is
100 m
,
find the height of the
building
.

(i)

100

m
(ii)

25

√

12

m
(iii)

50

m
(iv)

100

√

3

m
(v)

50

√

2

m

Question 6

6.

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 top of the
radio tower
is
10 m
,
find the distance between
the observation point and the foot of the
radio tower
.

(i)

6

m
(ii)

4

m
(iii)

3

m
(iv)

8

m
(v)

5

m

Question 7

7.

Two boys are on opposite sides of a tower of 40 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)

160
3

m
(ii)

160
3

√

3

m
(iii)

160
3

√

18

m
(iv)

80

√

2

m
(v)

160

m

Question 8

8.

A person, walking 20 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)

(

30

+

10

√

3

)

m
(ii)

600

m
(iii)

(

2

+

√

3

)

m
(iv)

(

15

√

6

+

15

√

2

)

m
(v)

(

30

√

6

+

10

√

18

)

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)

(

15

√

2

−

5

√

6

)

m
(ii)

(

2

−

√

3

)

m
(iii)

200

m
(iv)

(

10

√

3

−

10

)

m
(v)

(

10

√

18

−

10

√

6

)

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
5

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

(i)

75.00 m
(ii)

78.00 m
(iii)

72.00 m
(iv)

80.00 m
(v)

70.00 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)

(

6
7

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

(i)

87.43 m
(ii)

129.43 m
(iii)

124.43 m
(iv)

104.43 m
(v)

111.43 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)

(

4
9

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

(i)

6.89 m
(ii)

7.89 m
(iii)

9.89 m
(iv)

10.89 m
(v)

8.89 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)

(

5
3

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

(i)

12.00 m
(ii)

9.00 m
(iii)

15.00 m
(iv)

7.00 m
(v)

17.00 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)

(

10
7

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

(i)

66.43 m
(ii)

76.43 m
(iii)

74.43 m
(iv)

71.43 m
(v)

68.43 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
9

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

(i)

1290.00 m
(ii)

1560.00 m
(iii)

1320.00 m
(iv)

1440.00 m
(v)

1570.00 m

Question 16

16.

A
tower
stands vertically on the ground.

The distance between the observation point and its foot
tower
is
10

√

3

m
.

The distance between the observation point and its top
is
20

m
.

Find the angle of elevation.

(i)

30°
(ii)

90°
(iii)

75°
(iv)

60°
(v)

45°

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

(i)

29.14 m
(ii)

24.14 m
(iii)

27.14 m
(iv)

19.14 m
(v)

21.14 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 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 45° and 60° respectively. Find the width of the river .

(i)

125.69 m
(ii)

112.69 m
(iii)

94.69 m
(iv)

109.69 m
(v)

97.69 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 30° and 60° respectively. Find the height of the other temple.

(i)

114.66 m
(ii)

106.66 m
(iii)

90.66 m
(iv)

118.66 m
(v)

103.66 m

Question 20

20.

An observer 1.8 m tall, is 130 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)

133.80 m
(ii)

131.80 m
(iii)

149.80 m
(iv)

115.80 m
(v)

116.80 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 30° and 60° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

17.49 m

, distances away =

9.25 m

,

31.75 m
(ii)
height =

21.49 m

, distances away =

13.25 m

,

35.75 m
(iii)
height =

19.49 m

, distances away =

11.25 m

,

33.75 m
(iv)
height =

18.49 m

, distances away =

10.25 m

,

32.75 m
(v)
height =

20.49 m

, distances away =

12.25 m

,

34.75 m

Question 22

22.

From the top of a light house which is 90 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)

68.87 m
(ii)

70.87 m
(iii)

65.87 m
(iv)

62.87 m
(v)

60.87 m

Question 23

23.

From the top of a 12 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)

37.78 m
(ii)

35.78 m
(iii)

27.78 m
(iv)

29.78 m
(v)

32.78 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 100 m, find the height of the building .

(i)

160.21 m
(ii)

168.21 m
(iii)

173.21 m
(iv)

197.21 m
(v)

189.21 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 15 m, find the height of the flag staff .

(i)

10.98 m
(ii)

5.98 m
(iii)

15.98 m
(iv)

13.98 m
(v)

7.98 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 16 m, find the height of the building .

(i)

18.86 m
(ii)

16.86 m
(iii)

26.86 m
(iv)

24.86 m
(v)

21.86 m

Assignment Key