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
30°
.
If the height of the
building
is
170 m
,
find the distance between
the observation point and the top of the
building
.

(i)

341

m
(ii)

339

m
(iii)

340

m
(iv)

342

m
(v)

337

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

(i)

100

√

2

m
(ii)

200
3

√

3

m
(iii)

200
3

√

18

m
(iv)

200
3

m
(v)

200

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

(i)

199

m
(ii)

197

m
(iii)

201

m
(iv)

203

m
(v)

200

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
10 m
,
find the height of the
chimney
.

(i)

13

m
(ii)

10

m
(iii)

9

m
(iv)

11

m
(v)

8

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
50 m
,
find the height of the
tower
.

(i)

25

m
(ii)

75
2

√

2

m
(iii)

75

m
(iv)

25

√

18

m
(v)

25

√

3

m

Question 6

6.

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

(i)

85

√

3

m
(ii)

255
2

√

2

m
(iii)

85

√

18

m
(iv)

255

m
(v)

85

m

Question 7

7.

Two boys are on opposite sides of a tower of 80 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)

(

80

√

6

+

80

√

18

)

m
(ii)

(

−

12800

)

m
(iii)

(

40

√

6

+

120

√

2

)

m
(iv)

(

−

2

−

√

3

)

m
(v)

(

80

+

80

√

3

)

m

Question 8

8.

A person, walking 15 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
4

√

2

m
(ii)

15
2

m
(iii)

15
2

√

18

m
(iv)

15
2

√

3

m
(v)

45
2

m

Question 9

9.

A flagstaff stands on the top of a building at a distance of 50 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)

(

50

√

6

−

50
3

√

18

)

m
(ii)

5000
3

m
(iii)

(

25

√

6

−

25

√

2

)

m
(iv)

(

50

−

50
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)

(

7
8

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

(i)

64.25 m
(ii)

58.25 m
(iii)

56.25 m
(iv)

66.25 m
(v)

61.25 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)

(

5
6

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

(i)

71.67 m
(ii)

69.67 m
(iii)

63.67 m
(iv)

66.67 m
(v)

61.67 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
7

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

(i)

326.67 m
(ii)

340.67 m
(iii)

341.67 m
(iv)

300.67 m
(v)

319.67 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 height of the
tower
is
130 m
,
find the distance between
the observation point and the top of the
tower
.

(i)

209.00 m
(ii)

195.00 m
(iii)

180.00 m
(iv)

217.00 m
(v)

188.00 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
50 m
,
find the distance between
the observation point and the top of the
tower
.

(i)

83.33 m
(ii)

80.33 m
(iii)

88.33 m
(iv)

78.33 m
(v)

86.33 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)

(

1
9

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

(i)

3.56 m
(ii)

5.56 m
(iii)

6.56 m
(iv)

7.56 m
(v)

4.56 m

Question 16

16.

A
tower
stands vertically on the ground.

The height of the
tower
is
140

√

3

m
.

The distance between the observation point and its foot
is
420

m
.

Find the angle of elevation.

(i)

30°
(ii)

60°
(iii)

90°
(iv)

75°
(v)

45°

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

(i)

111.57 m
(ii)

161.57 m
(iii)

134.57 m
(iv)

138.57 m
(v)

152.57 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 70 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)

67.00 m
(ii)

70.00 m
(iii)

75.00 m
(iv)

65.00 m
(v)

73.00 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 20 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)

10.45 m
(ii)

9.45 m
(iii)

8.45 m
(iv)

7.45 m
(v)

6.45 m

Question 20

20.

An observer 1.3 m tall, is 20 m away from a tower . The angle of elevation of the top of the tower from her eyes is 60°. Find the height of the tower .

(i)

35.94 m
(ii)

38.94 m
(iii)

30.94 m
(iv)

40.94 m
(v)

32.94 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 30° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

18.32 m

, distances away =

31 m

,

11 m
(ii)
height =

16.32 m

, distances away =

29 m

,

9 m
(iii)
height =

17.32 m

, distances away =

30 m

,

10 m
(iv)
height =

19.32 m

, distances away =

32 m

,

12 m
(v)
height =

15.32 m

, distances away =

28 m

,

8 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)

68.50 m
(ii)

58.50 m
(iii)

60.50 m
(iv)

66.50 m
(v)

63.50 m

Question 23

23.

From the top of a 17 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)

49.45 m
(ii)

51.45 m
(iii)

43.45 m
(iv)

41.45 m
(v)

46.45 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 70 m, find the height of the building .

(i)

40.41 m
(ii)

45.41 m
(iii)

43.41 m
(iv)

37.41 m
(v)

35.41 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 9 m, find the height of the flag staff .

(i)

23.00 m
(ii)

21.00 m
(iii)

15.00 m
(iv)

13.00 m
(v)

18.00 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 10 m, find the height of the building .

(i)

7.00 m
(ii)

5.00 m
(iii)

4.00 m
(iv)

6.00 m
(v)

3.00 m

Assignment Key