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
200 m
,
find the distance between
the observation point and the top of the
chimney
.

(i)

400

m
(ii)

400
3

√

3

m
(iii)

200

√

2

m
(iv)

400
3

m
(v)

400
3

√

18

m

Question 2

2.

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
170 m
,
find the distance between
the observation point and the foot of the
building
.

(i)

170

√

18

m
(ii)

170

m
(iii)

170

√

3

m
(iv)

510

m
(v)

255

√

2

m

Question 3

3.

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

(i)

400

m
(ii)

400

√

3

m
(iii)

200

m
(iv)

100

√

12

m
(v)

200

√

2

m

Question 4

4.

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 foot of the
chimney
is
160 m
,
find the height of the
chimney
.

(i)

159

m
(ii)

163

m
(iii)

161

m
(iv)

160

m
(v)

158

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

(i)

100

m
(ii)

50

√

12

m
(iii)

200

√

3

m
(iv)

200

m
(v)

100

√

2

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

√

3

m
(iii)

55

√

18

m
(iv)

165
2

√

2

m
(v)

165

m

Question 7

7.

Two boys are on opposite sides of a tower of 10 m height. They measure the angle of elevation of the top of the tower as 45° and 30° respectively. Find the distance between the two boys.

(i)

(

5

√

6

+

15

√

2

)

m
(ii)

(

10

+

10

√

3

)

m
(iii)

(

−

200

)

m
(iv)

(

−

2

−

√

3

)

m
(v)

(

10

√

6

+

10

√

18

)

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
2

√

6

+

45
2

√

2

)

m
(ii)

1350

m
(iii)

(

2

+

√

3

)

m
(iv)

(

45

+

15

√

3

)

m
(v)

(

45

√

6

+

15

√

18

)

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 45°. Find the height of the flagstaff .

(i)

(

75
2

√

2

−

25
2

√

6

)

m
(ii)

(

2

−

√

3

)

m
(iii)

1250

m
(iv)

(

25

√

3

−

25

)

m
(v)

(

25

√

18

−

25

√

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
2

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

(i)

280.00 m
(ii)

288.00 m
(iii)

266.00 m
(iv)

273.00 m
(v)

295.00 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)

(

2
3

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

(i)

20.00 m
(ii)

15.00 m
(iii)

12.00 m
(iv)

18.00 m
(v)

10.00 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
6

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

(i)

161.00 m
(ii)

143.00 m
(iii)

156.00 m
(iv)

168.00 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)

(

4
3

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

(i)

43.00 m
(ii)

45.00 m
(iii)

35.00 m
(iv)

37.00 m
(v)

40.00 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)

(

11
6

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

(i)

49.55 m
(ii)

51.55 m
(iii)

57.55 m
(iv)

54.55 m
(v)

59.55 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
7

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

(i)

54.43 m
(ii)

56.43 m
(iii)

46.43 m
(iv)

48.43 m
(v)

51.43 m

Question 16

16.

A
tower
stands vertically on the ground.

The distance between the observation point and its foot
tower
is
170

√

2

m
.

The distance between the observation point and its top
is
340

m
.

Find the angle of elevation.

(i)

45°
(ii)

105°
(iii)

75°
(iv)

30°
(v)

60°

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

(i)

144.85 m
(ii)

120.85 m
(iii)

126.85 m
(iv)

156.85 m
(v)

169.85 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 130 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 width of the river .

(i)

78.05 m
(ii)

72.05 m
(iii)

70.05 m
(iv)

75.05 m
(v)

80.05 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 120 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 height of the other temple.

(i)

45.71 m
(ii)

47.71 m
(iii)

55.71 m
(iv)

53.71 m
(v)

50.71 m

Question 20

20.

An observer 1.4 m tall, is 170 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)

188.40 m
(ii)

171.40 m
(iii)

156.40 m
(iv)

159.40 m
(v)

185.40 m

Question 21

21.

Two poles of equal height are standing opposite to each other on either side of a road which is 20 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

10.66 m

, distances away =

17 m

,

7 m
(ii)
height =

6.66 m

, distances away =

13 m

,

3 m
(iii)
height =

8.66 m

, distances away =

15 m

,

5 m
(iv)
height =

9.66 m

, distances away =

16 m

,

6 m
(v)
height =

7.66 m

, distances away =

14 m

,

4 m

Question 22

22.

From the top of a light house which is 60 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)

22.36 m
(ii)

25.36 m
(iii)

20.36 m
(iv)

30.36 m
(v)

28.36 m

Question 23

23.

From the top of a 7 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 45°. Find the height of the cable tower.

(i)

14.12 m
(ii)

16.12 m
(iii)

24.12 m
(iv)

22.12 m
(v)

19.12 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 35 m, find the height of the building .

(i)

20.21 m
(ii)

25.21 m
(iii)

23.21 m
(iv)

17.21 m
(v)

15.21 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 17 m, find the height of the flag staff .

(i)

7.45 m
(ii)

9.45 m
(iii)

17.45 m
(iv)

12.45 m
(v)

15.45 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 12 m, find the height of the building .

(i)

4.00 m
(ii)

7.00 m
(iii)

8.00 m
(iv)

5.00 m
(v)

6.00 m

Assignment Key