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
60°
.
If the height of the
radio tower
is
150 m
,
find the distance between
the observation point and the top of the
radio tower
.

(i)

100

√

3

m
(ii)

300

m
(iii)

150

√

2

m
(iv)

100

m
(v)

100

√

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

(i)

130

m
(ii)

390

m
(iii)

195

√

2

m
(iv)

130

√

3

m
(v)

130

√

18

m

Question 3

3.

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

(i)

260

m
(ii)

130

√

2

m
(iii)

65

√

12

m
(iv)

260

√

3

m
(v)

130

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
20 m
,
find the height of the
chimney
.

(i)

22

m
(ii)

19

m
(iii)

21

m
(iv)

20

m
(v)

17

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

(i)

120

m
(ii)

60

√

2

m
(iii)

40

√

18

m
(iv)

40

√

3

m
(v)

40

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)

25
2

√

12

m
(ii)

25

m
(iii)

50

√

3

m
(iv)

50

m
(v)

25

√

2

m

Question 7

7.

Two boys are on opposite sides of a tower of 110 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)

220

√

2

m
(ii)

440
3

√

3

m
(iii)

440
3

m
(iv)

440

m
(v)

440
3

√

18

m

Question 8

8.

A person, walking 35 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)

(

35
2

√

18

+

35
2

√

6

)

m
(ii)

1225
2

m
(iii)

(

35
2

√

3

+

35
2

)

m
(iv)

(

105
4

√

2

+

35
4

√

6

)

m
(v)

(

2

+

√

3

)

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 30°. Find the height of the flagstaff .

(i)

20

√

18

m
(ii)

30

√

2

m
(iii)

20

√

3

m
(iv)

60

m
(v)

20

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)

(

2
3

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

(i)

109.67 m
(ii)

132.67 m
(iii)

121.67 m
(iv)

138.67 m
(v)

126.67 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)

(

1
2

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

(i)

355.00 m
(ii)

380.00 m
(iii)

376.00 m
(iv)

398.00 m
(v)

404.00 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
2

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

(i)

90.00 m
(ii)

85.00 m
(iii)

95.00 m
(iv)

93.00 m
(v)

87.00 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)

(

5
3

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

(i)

134.67 m
(ii)

133.67 m
(iii)

93.67 m
(iv)

116.67 m
(v)

111.67 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)

(

3
2

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

(i)

106.67 m
(ii)

92.67 m
(iii)

99.67 m
(iv)

124.67 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)

(

6
7

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

(i)

145.71 m
(ii)

162.71 m
(iii)

131.71 m
(iv)

149.71 m
(v)

130.71 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)

30°
(ii)

45°
(iii)

90°
(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 30° with the ground. The top of the tree touches the ground at a distance of 30 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

51.96 m
(ii)

48.96 m
(iii)

56.96 m
(iv)

46.96 m
(v)

54.96 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 90 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 width of the river .

(i)

56.96 m
(ii)

46.96 m
(iii)

48.96 m
(iv)

51.96 m
(v)

54.96 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 140 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)

62.17 m
(ii)

59.17 m
(iii)

54.17 m
(iv)

56.17 m
(v)

64.17 m

Question 20

20.

An observer 1.9 m tall, is 40 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)

46.90 m
(ii)

44.90 m
(iii)

41.90 m
(iv)

38.90 m
(v)

36.90 m

Question 21

21.

Two poles of equal height are standing opposite to each other on either side of a road which is 10 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 =

6.34 m

, distances away =

3.66 m

,

6.34 m
(ii)
height =

4.34 m

, distances away =

1.66 m

,

4.34 m
(iii)
height =

5.34 m

, distances away =

2.66 m

,

5.34 m
(iv)
height =

8.34 m

, distances away =

5.66 m

,

8.34 m
(v)
height =

7.34 m

, distances away =

4.66 m

,

7.34 m

Question 22

22.

From the top of a light house which is 100 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)

42.27 m
(ii)

45.27 m
(iii)

37.27 m
(iv)

47.27 m
(v)

39.27 m

Question 23

23.

From the top of a 11 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)

27.05 m
(ii)

30.05 m
(iii)

33.05 m
(iv)

35.05 m
(v)

25.05 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 65 m, find the height of the building .

(i)

104.59 m
(ii)

98.59 m
(iii)

124.59 m
(iv)

129.59 m
(v)

112.59 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 11 m, find the height of the flag staff .

(i)

25.00 m
(ii)

22.00 m
(iii)

27.00 m
(iv)

17.00 m
(v)

19.00 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 30°. If the height of the flag staff is 14 m, find the height of the building .

(i)

5.00 m
(ii)

7.00 m
(iii)

6.00 m
(iv)

8.00 m
(v)

9.00 m

Assignment Key