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

(i)

120

√

3

m
(ii)

180

√

2

m
(iii)

360

m
(iv)

120

m
(v)

120

√

18

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

(i)

188

m
(ii)

192

m
(iii)

190

m
(iv)

189

m
(v)

191

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

(i)

283

m
(ii)

279

m
(iii)

281

m
(iv)

278

m
(v)

280

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)

60

√

18

m
(ii)

60

√

3

m
(iii)

90

√

2

m
(iv)

180

m
(v)

60

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
40 m
,
find the height of the
chimney
.

(i)

20

√

18

m
(ii)

20

m
(iii)

30

√

2

m
(iv)

20

√

3

m
(v)

60

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
45°
.
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)

5

√

2

m
(ii)

5
2

√

12

m
(iii)

10

√

3

m
(iv)

5

m
(v)

10

m

Question 7

7.

Two boys are on opposite sides of a tower of 190 m height. They measure the angle of elevation of the top of the tower as 30° and 45° respectively. Find the distance between the two boys.

(i)

(

190

√

3

+

190

)

m
(ii)

(

2

+

√

3

)

m
(iii)

72200

m
(iv)

(

190

√

18

+

190

√

6

)

m
(v)

(

285

√

2

+

95

√

6

)

m

Question 8

8.

A person, walking 30 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)

(

45

+

15

√

3

)

m
(ii)

(

45
2

√

6

+

45
2

√

2

)

m
(iii)

(

2

+

√

3

)

m
(iv)

1350

m
(v)

(

45

√

6

+

15

√

18

)

m

Question 9

9.

A flagstaff stands on the top of a building at a distance of 30 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)

(

30

√

18

−

30

√

6

)

m
(ii)

1800

m
(iii)

(

2

−

√

3

)

m
(iv)

(

30

√

3

−

30

)

m
(v)

(

45

√

2

−

15

√

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)

(

1
3

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

(i)

8.67 m
(ii)

4.67 m
(iii)

6.67 m
(iv)

7.67 m
(v)

5.67 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
10 m
,
find the distance between
the observation point and the foot of the
tower
.

(i)

8.57 m
(ii)

9.57 m
(iii)

10.57 m
(iv)

7.57 m
(v)

6.57 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
30 m
,
find the height of the
tower
.

(i)

12.00 m
(ii)

15.00 m
(iii)

10.00 m
(iv)

18.00 m
(v)

20.00 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)

(

16
9

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

(i)

23.12 m
(ii)

25.12 m
(iii)

33.12 m
(iv)

31.12 m
(v)

28.12 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)

(

7
4

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

(i)

31.29 m
(ii)

29.29 m
(iii)

37.29 m
(iv)

34.29 m
(v)

39.29 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)

(

2
3

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

(i)

63.67 m
(ii)

69.67 m
(iii)

61.67 m
(iv)

71.67 m
(v)

66.67 m

Question 16

16.

A
tower
stands vertically on the ground.

The height of the
tower
is
160

m
.

The distance between the observation point and its foot
is
160

m
.

Find the angle of elevation.

(i)

75°
(ii)

45°
(iii)

30°
(iv)

105°
(v)

60°

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

(i)

557.82 m
(ii)

543.82 m
(iii)

567.82 m
(iv)

559.82 m
(v)

585.82 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 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 45° respectively. Find the width of the river .

(i)

15.00 m
(ii)

13.00 m
(iii)

7.00 m
(iv)

5.00 m
(v)

10.00 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 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 30° and 60° respectively. Find the height of the other temple.

(i)

112.66 m
(ii)

134.66 m
(iii)

126.66 m
(iv)

154.66 m
(v)

111.66 m

Question 20

20.

An observer 1.6 m tall, is 150 m away from a tower . The angle of elevation of the top of the tower from her eyes is 30°. Find the height of the tower .

(i)

85.21 m
(ii)

93.21 m
(iii)

91.21 m
(iv)

83.21 m
(v)

88.21 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 45° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

5.49 m

, distances away =

5.49 m

,

9.51 m
(ii)
height =

6.49 m

, distances away =

6.49 m

,

10.51 m
(iii)
height =

3.49 m

, distances away =

3.49 m

,

7.51 m
(iv)
height =

4.49 m

, distances away =

4.49 m

,

8.51 m
(v)
height =

7.49 m

, distances away =

7.49 m

,

11.51 m

Question 22

22.

From the top of a light house which is 50 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)

26.13 m
(ii)

21.13 m
(iii)

24.13 m
(iv)

18.13 m
(v)

16.13 m

Question 23

23.

From the top of a 13 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)

32.51 m
(ii)

35.51 m
(iii)

40.51 m
(iv)

38.51 m
(v)

30.51 m

Question 24

24.

The angle of elevation of the top of a building from the foot of a tower is 30°. 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 55 m, find the height of the building .

(i)

36.76 m
(ii)

28.76 m
(iii)

26.76 m
(iv)

31.76 m
(v)

34.76 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 12 m, find the height of the flag staff .

(i)

19.00 m
(ii)

21.00 m
(iii)

24.00 m
(iv)

27.00 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 45°. If the height of the flag staff is 11 m, find the height of the building .

(i)

12.03 m
(ii)

10.03 m
(iii)

15.03 m
(iv)

20.03 m
(v)

18.03 m

Assignment Key