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
50 m
,
find the distance between
the observation point and the top of the
building
.

(i)

100
3

m
(ii)

100
3

√

3

m
(iii)

100

m
(iv)

50

√

2

m
(v)

100
3

√

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

(i)

360

m
(ii)

180

√

2

m
(iii)

120

m
(iv)

120

√

18

m
(v)

120

√

3

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

(i)

60

m
(ii)

60

√

2

m
(iii)

120

m
(iv)

30

√

12

m
(v)

120

√

3

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
190 m
,
find the height of the
radio tower
.

(i)

190

√

3

m
(ii)

190

m
(iii)

190

√

18

m
(iv)

285

√

2

m
(v)

570

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
130 m
,
find the height of the
tower
.

(i)

65

√

2

m
(ii)

130

m
(iii)

130

√

3

m
(iv)

65

m
(v)

65
2

√

12

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

(i)

84

m
(ii)

86

m
(iii)

88

m
(iv)

82

m
(v)

85

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 60° respectively. Find the distance between the two boys.

(i)

760
3

m
(ii)

760
3

√

18

m
(iii)

760

m
(iv)

760
3

√

3

m
(v)

380

√

2

m

Question 8

8.

A person, walking 45 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)

45
2

m
(ii)

135
4

√

2

m
(iii)

135
2

m
(iv)

45
2

√

18

m
(v)

45
2

√

3

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

(i)

(

35

√

6

−

35
3

√

18

)

m
(ii)

2450
3

m
(iii)

(

35
2

√

6

−

35
2

√

2

)

m
(iv)

(

35

−

35
3

√

3

)

m
(v)

(

2

−

√

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
2

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

(i)

7.00 m
(ii)

3.00 m
(iii)

6.00 m
(iv)

4.00 m
(v)

5.00 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
30 m
,
find the distance between
the observation point and the top of the
tower
.

(i)

42.00 m
(ii)

48.00 m
(iii)

50.00 m
(iv)

45.00 m
(v)

40.00 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
4

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

(i)

468.00 m
(ii)

480.00 m
(iii)

486.00 m
(iv)

497.00 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)

(

7
6

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

(i)

86.67 m
(ii)

81.67 m
(iii)

76.67 m
(iv)

84.67 m
(v)

78.67 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)

(

15
8

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

(i)

387.00 m
(ii)

372.00 m
(iii)

353.00 m
(iv)

375.00 m
(v)

382.00 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)

(

1
2

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

(i)

55.00 m
(ii)

65.00 m
(iii)

63.00 m
(iv)

60.00 m
(v)

57.00 m

Question 16

16.

A
tower
stands vertically on the ground.

The height of the
tower
is
190

√

3

m
.

The distance between the observation point and its foot
is
570

m
.

Find the angle of elevation.

(i)

60°
(ii)

75°
(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 45° 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)

69.43 m
(ii)

67.43 m
(iii)

77.43 m
(iv)

75.43 m
(v)

72.43 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 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 width of the river .

(i)

87.69 m
(ii)

124.69 m
(iii)

96.69 m
(iv)

109.69 m
(v)

111.69 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 160 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)

72.63 m
(ii)

70.63 m
(iii)

64.63 m
(iv)

62.63 m
(v)

67.63 m

Question 20

20.

An observer 1.7 m tall, is 100 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)

54.44 m
(ii)

64.44 m
(iii)

59.44 m
(iv)

56.44 m
(v)

62.44 m

Question 21

21.

Two poles of equal height are standing opposite to each other on either side of a road which is 40 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 45° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

26.36 m

, distances away =

26.36 m

,

15.64 m
(ii)
height =

23.36 m

, distances away =

23.36 m

,

12.64 m
(iii)
height =

25.36 m

, distances away =

25.36 m

,

14.64 m
(iv)
height =

27.36 m

, distances away =

27.36 m

,

16.64 m
(v)
height =

24.36 m

, distances away =

24.36 m

,

13.64 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)

28.36 m
(ii)

25.36 m
(iii)

22.36 m
(iv)

20.36 m
(v)

30.36 m

Question 23

23.

From the top of a 12 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)

32.79 m
(ii)

29.79 m
(iii)

37.79 m
(iv)

35.79 m
(v)

27.79 m

Question 24

24.

The angle of elevation of the top of a building from the foot of a tower is 45°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 90 m, find the height of the building .

(i)

46.96 m
(ii)

56.96 m
(iii)

54.96 m
(iv)

51.96 m
(v)

48.96 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)

27.00 m
(iii)

19.00 m
(iv)

22.00 m
(v)

17.00 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 45° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 10 m, find the height of the building .

(i)

13.66 m
(ii)

8.66 m
(iii)

18.66 m
(iv)

10.66 m
(v)

16.66 m

Assignment Key