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
50 m
,
find the distance between
the observation point and the top of the
building
.

(i)

101

m
(ii)

99

m
(iii)

100

m
(iv)

98

m
(v)

102

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
45°
.
If the height of the
tower
is
10 m
,
find the distance between
the observation point and the foot of the
tower
.

(i)

9

m
(ii)

13

m
(iii)

7

m
(iv)

11

m
(v)

10

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
30 m
,
find the distance between
the observation point and the top of the
tower
.

(i)

60

m
(ii)

30

√

2

m
(iii)

20

m
(iv)

20

√

3

m
(v)

20

√

18

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

(i)

8

m
(ii)

11

m
(iii)

13

m
(iv)

10

m
(v)

9

m

Question 5

5.

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
90 m
,
find the height of the
chimney
.

(i)

45

√

3

m
(ii)

45

m
(iii)

45

√

18

m
(iv)

135

m
(v)

135
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
45°
.
If the distance between the point and the top of the
chimney
is
50 m
,
find the distance between
the observation point and the foot of the
chimney
.

(i)

50

m
(ii)

25

√

2

m
(iii)

25
2

√

12

m
(iv)

50

√

3

m
(v)

25

m

Question 7

7.

Two boys are on opposite sides of a tower of 180 m height. They measure the angle of elevation of the top of the tower as 30° and 60° respectively. Find the distance between the two boys.

(i)

720

m
(ii)

240

m
(iii)

360

√

2

m
(iv)

240

√

18

m
(v)

240

√

3

m

Question 8

8.

A person, walking 40 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)

800

m
(ii)

(

20

√

18

+

20

√

6

)

m
(iii)

(

2

+

√

3

)

m
(iv)

(

30

√

2

+

10

√

6

)

m
(v)

(

20

√

3

+

20

)

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 30°. Find the height of the flagstaff .

(i)

20

m
(ii)

20
3

m
(iii)

10

√

2

m
(iv)

20
3

√

3

m
(v)

20
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)

(

4
7

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

(i)

5.71 m
(ii)

4.71 m
(iii)

3.71 m
(iv)

6.71 m
(v)

7.71 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)

(

7
8

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

(i)

12.50 m
(ii)

17.50 m
(iii)

22.50 m
(iv)

14.50 m
(v)

20.50 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)

(

2
3

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

(i)

6.67 m
(ii)

8.67 m
(iii)

7.67 m
(iv)

4.67 m
(v)

5.67 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)

(

10
7

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

(i)

80.00 m
(ii)

74.00 m
(iii)

82.00 m
(iv)

77.00 m
(v)

72.00 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)

(

5
4

)
.
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)

65.50 m
(ii)

57.50 m
(iii)

59.50 m
(iv)

62.50 m
(v)

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

(i)

68.00 m
(ii)

65.00 m
(iii)

60.00 m
(iv)

62.00 m
(v)

70.00 m

Question 16

16.

A
tower
stands vertically on the ground.

The height of the
tower
is
200

√

3

m
.

The distance between the observation point and its top
is
400

m
.

Find the angle of elevation.

(i)

60°
(ii)

105°
(iii)

45°
(iv)

30°
(v)

90°

Question 17

17.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60° 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)

34.32 m
(ii)

32.32 m
(iii)

42.32 m
(iv)

37.32 m
(v)

40.32 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 180 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)

180.00 m
(ii)

165.00 m
(iii)

157.00 m
(iv)

198.00 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 100 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)

45.27 m
(ii)

47.27 m
(iii)

37.27 m
(iv)

39.27 m
(v)

42.27 m

Question 20

20.

An observer 1.8 m tall, is 20 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)

33.44 m
(ii)

39.44 m
(iii)

31.44 m
(iv)

41.44 m
(v)

36.44 m

Question 21

21.

Two poles of equal height are standing opposite to each other on either side of a road which is 25 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30° and 45° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

7.15 m

, distances away =

7.15 m

,

13.85 m
(ii)
height =

10.15 m

, distances away =

10.15 m

,

16.85 m
(iii)
height =

8.15 m

, distances away =

8.15 m

,

14.85 m
(iv)
height =

9.15 m

, distances away =

9.15 m

,

15.85 m
(v)
height =

11.15 m

, distances away =

11.15 m

,

17.85 m

Question 22

22.

From the top of a light house which is 25 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)

23.86 m
(ii)

25.86 m
(iii)

33.86 m
(iv)

28.86 m
(v)

31.86 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 85 m, find the height of the building .

(i)

145.21 m
(ii)

154.21 m
(iii)

161.21 m
(iv)

129.21 m
(v)

147.21 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 19 m, find the height of the flag staff .

(i)

16.91 m
(ii)

13.91 m
(iii)

18.91 m
(iv)

8.91 m
(v)

10.91 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 19 m, find the height of the building .

(i)

10.50 m
(ii)

7.50 m
(iii)

9.50 m
(iv)

8.50 m
(v)

11.50 m

Assignment Key