EduSahara™ Worksheet

Question 1

1.

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

(i)

260

m
(ii)

65

√

12

m
(iii)

130

√

2

m
(iv)

260

√

3

m
(v)

130

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

(i)

100
3

m
(ii)

50

√

2

m
(iii)

100
3

√

18

m
(iv)

100
3

√

3

m
(v)

100

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

(i)

40

√

12

m
(ii)

80

√

2

m
(iii)

160

√

3

m
(iv)

160

m
(v)

80

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
180 m
,
find the height of the
chimney
.

(i)

180

m
(ii)

179

m
(iii)

183

m
(iv)

181

m
(v)

177

m

Question 5

5.

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
190 m
,
find the height of the
radio tower
.

(i)

95

√

3

m
(ii)

95

√

18

m
(iii)

95

m
(iv)

285

m
(v)

285
2

√

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
30°
.
If the distance between the point and the top of the
radio tower
is
130 m
,
find the distance between
the observation point and the foot of the
radio tower
.

(i)

195
2

√

2

m
(ii)

65

√

3

m
(iii)

65

√

18

m
(iv)

65

m
(v)

195

m

Question 7

7.

Two boys are on opposite sides of a tower of 70 m height. They measure the angle of elevation of the top of the tower as 45° and 60° respectively. Find the distance between the two boys.

(i)

(

2

+

√

3

)

m
(ii)

(

35

√

6

+

35

√

2

)

m
(iii)

(

70

√

6

+

70
3

√

18

)

m
(iv)

(

70

+

70
3

√

3

)

m
(v)

9800
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)

(

30

√

2

+

10

√

6

)

m
(iv)

(

2

+

√

3

)

m
(v)

(

20

√

3

+

20

)

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 45° and the angle of elevation of the top of the building is 30°. Find the height of the flagstaff .

(i)

(

25

√

6

−

25
3

√

18

)

m
(ii)

1250
3

m
(iii)

(

2

−

√

3

)

m
(iv)

(

25
2

√

6

−

25
2

√

2

)

m
(v)

(

25

−

25
3

√

3

)

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
5

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

(i)

350.00 m
(ii)

365.00 m
(iii)

342.00 m
(iv)

323.00 m
(v)

364.00 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)

(

3
5

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

(i)

283.33 m
(ii)

290.33 m
(iii)

265.33 m
(iv)

307.33 m
(v)

261.33 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)

(

3
4

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

(i)

88.33 m
(ii)

90.33 m
(iii)

96.33 m
(iv)

93.33 m
(v)

98.33 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)

(

6
5

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

(i)

29.00 m
(ii)

21.00 m
(iii)

19.00 m
(iv)

27.00 m
(v)

24.00 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
100 m
,
find the distance between
the observation point and the top of the
tower
.

(i)

130.86 m
(ii)

127.86 m
(iii)

146.86 m
(iv)

158.86 m
(v)

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

(i)

225.00 m
(ii)

252.00 m
(iii)

268.00 m
(iv)

227.00 m
(v)

240.00 m

Question 16

16.

A
tower
stands vertically on the ground.

The height of the
tower
is
170

√

3

m
.

The distance between the observation point and its foot
is
510

m
.

Find the angle of elevation.

(i)

75°
(ii)

30°
(iii)

45°
(iv)

60°
(v)

90°

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

(i)

325.85 m
(ii)

313.85 m
(iii)

298.85 m
(iv)

289.85 m
(v)

327.85 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 40 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)

23.09 m
(ii)

28.09 m
(iii)

20.09 m
(iv)

18.09 m
(v)

26.09 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 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 60° respectively. Find the height of the other temple.

(i)

147.00 m
(ii)

124.00 m
(iii)

120.00 m
(iv)

102.00 m

Question 20

20.

An observer 1.4 m tall, is 200 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)

201.40 m
(ii)

224.40 m
(iii)

186.40 m
(iv)

204.40 m
(v)

197.40 m

Question 21

21.

Two poles of equal height are standing opposite to each other on either side of a road which is 5 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 =

3.83 m

, distances away =

3.83 m

,

5.17 m
(ii)
height =

0.83 m

, distances away =

0.83 m

,

2.17 m
(iii)
height =

9.83 m

, distances away =

9.83 m

,

1.17 m
(iv)
height =

1.83 m

, distances away =

1.83 m

,

3.17 m
(v)
height =

2.83 m

, distances away =

2.83 m

,

4.17 m

Question 22

22.

From the top of a light house which is 55 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)

60.50 m
(ii)

68.50 m
(iii)

66.50 m
(iv)

63.50 m
(v)

58.50 m

Question 23

23.

From the top of a 9 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)

27.59 m
(ii)

19.59 m
(iii)

24.59 m
(iv)

29.59 m
(v)

21.59 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)

177.21 m
(ii)

173.21 m
(iii)

196.21 m
(iv)

151.21 m
(v)

171.21 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 11 m, find the height of the flag staff .

(i)

10.05 m
(ii)

8.05 m
(iii)

9.05 m
(iv)

7.05 m
(v)

6.05 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)

7.50 m
(ii)

8.50 m
(iii)

10.50 m
(iv)

11.50 m
(v)

9.50 m

Assignment Key