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

(i)

20

√

2

m
(ii)

40

m
(iii)

40
3

√

18

m
(iv)

40
3

m
(v)

40
3

√

3

m

Question 2

2.

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 height of the
chimney
is
150 m
,
find the distance between
the observation point and the foot of the
chimney
.

(i)

153

m
(ii)

151

m
(iii)

147

m
(iv)

149

m
(v)

150

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

(i)

137

m
(ii)

141

m
(iii)

139

m
(iv)

140

m
(v)

143

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
30 m
,
find the height of the
chimney
.

(i)

29

m
(ii)

33

m
(iii)

31

m
(iv)

30

m
(v)

28

m

Question 5

5.

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 top of the
tower
is
20 m
,
find the height of the
tower
.

(i)

10

√

2

m
(ii)

5

√

12

m
(iii)

20

√

3

m
(iv)

20

m
(v)

10

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
45°
.
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)

50

√

2

m
(ii)

25

√

12

m
(iii)

100

m
(iv)

100

√

3

m
(v)

50

m

Question 7

7.

Two boys are on opposite sides of a tower of 50 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)

200
3

√

18

m
(ii)

100

√

2

m
(iii)

200
3

√

3

m
(iv)

200

m
(v)

200
3

m

Question 8

8.

A person, walking 20 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 60°. Find the height of the flagpost .

(i)

30

m
(ii)

15

√

2

m
(iii)

10

m
(iv)

10

√

3

m
(v)

10

√

18

m

Question 9

9.

A flagstaff stands on the top of a building at a distance of 35 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)

70
3

√

3

m
(ii)

70
3

√

18

m
(iii)

70
3

m
(iv)

70

m
(v)

35

√

2

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
9

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

(i)

440.50 m
(ii)

411.50 m
(iii)

424.50 m
(iv)

427.50 m
(v)

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

(i)

118.00 m
(ii)

120.00 m
(iii)

96.00 m
(iv)

142.00 m
(v)

135.00 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)

(

1
3

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

(i)

13.67 m
(ii)

11.67 m
(iii)

19.67 m
(iv)

16.67 m
(v)

21.67 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)

(

3
2

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

(i)

45.00 m
(ii)

43.00 m
(iii)

40.00 m
(iv)

35.00 m
(v)

37.00 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
3

)
.
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)

261.33 m
(ii)

215.33 m
(iii)

233.33 m
(iv)

240.33 m
(v)

229.33 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)

(

3
4

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

(i)

136.00 m
(ii)

165.00 m
(iii)

150.00 m
(iv)

133.00 m
(v)

163.00 m

Question 16

16.

A
tower
stands vertically on the ground.

The distance between the observation point and its foot
tower
is
180

m
.

The distance between the observation point and its top
is
360

m
.

Find the angle of elevation.

(i)

105°
(ii)

60°
(iii)

45°
(iv)

90°
(v)

30°

Question 17

17.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 30° with the ground. The top of the tree touches the ground at a distance of 110 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

190.53 m
(ii)

202.53 m
(iii)

175.53 m
(iv)

162.53 m
(v)

206.53 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)

5.00 m
(ii)

15.00 m
(iii)

10.00 m
(iv)

13.00 m
(v)

7.00 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 200 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)

89.53 m
(ii)

87.53 m
(iii)

79.53 m
(iv)

81.53 m
(v)

84.53 m

Question 20

20.

An observer 1.9 m tall, is 150 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)

151.90 m
(ii)

129.90 m
(iii)

158.90 m
(iv)

167.90 m
(v)

134.90 m

Question 21

21.

Two poles of equal height are standing opposite to each other on either side of a road which is 50 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 45° and 60° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

32.7 m

, distances away =

19.3 m

,

32.7 m
(ii)
height =

31.7 m

, distances away =

18.3 m

,

31.7 m
(iii)
height =

33.7 m

, distances away =

20.3 m

,

33.7 m
(iv)
height =

29.7 m

, distances away =

16.3 m

,

29.7 m
(v)
height =

30.7 m

, distances away =

17.3 m

,

30.7 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)

33.86 m
(iii)

28.86 m
(iv)

31.86 m
(v)

25.86 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)

40.51 m
(ii)

32.51 m
(iii)

38.51 m
(iv)

30.51 m
(v)

35.51 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 40 m, find the height of the building .

(i)

26.10 m
(ii)

20.10 m
(iii)

23.10 m
(iv)

28.10 m
(v)

18.10 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 12 m, find the height of the flag staff .

(i)

7.79 m
(ii)

10.79 m
(iii)

8.79 m
(iv)

6.79 m
(v)

9.79 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 13 m, find the height of the building .

(i)

20.76 m
(ii)

22.76 m
(iii)

14.76 m
(iv)

17.76 m
(v)

12.76 m

Assignment Key