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
45°
.
If the height of the
chimney
is
120 m
,
find the distance between
the observation point and the top of the
chimney
.

(i)

120

√

2

m
(ii)

60

√

12

m
(iii)

240

m
(iv)

240

√

3

m
(v)

120

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

(i)

160

√

18

m
(ii)

160

m
(iii)

160

√

3

m
(iv)

480

m
(v)

240

√

2

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

(i)

10

√

12

m
(ii)

40

√

3

m
(iii)

40

m
(iv)

20

m
(v)

20

√

2

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
30°
.
If the distance between the point and the foot of the
chimney
is
10 m
,
find the height of the
chimney
.

(i)

10

m
(ii)

10
3

m
(iii)

10
3

√

3

m
(iv)

10
3

√

18

m
(v)

5

√

2

m

Question 5

5.

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 distance between the point and the top of the
building
is
40 m
,
find the height of the
building
.

(i)

30

√

2

m
(ii)

60

m
(iii)

20

m
(iv)

20

√

3

m
(v)

20

√

18

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

(i)

15

√

18

m
(ii)

15

m
(iii)

15

√

3

m
(iv)

45

m
(v)

45
2

√

2

m

Question 7

7.

Two boys are on opposite sides of a tower of 130 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)

520

m
(ii)

520
3

√

18

m
(iii)

260

√

2

m
(iv)

520
3

√

3

m
(v)

520
3

m

Question 8

8.

A person, walking 25 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)

25
2

m
(ii)

25
2

√

18

m
(iii)

25
2

√

3

m
(iv)

75
4

√

2

m
(v)

75
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 60° and the angle of elevation of the top of the building is 30°. Find the height of the flagstaff .

(i)

100

m
(ii)

100
3

√

3

m
(iii)

50

√

2

m
(iv)

100
3

√

18

m
(v)

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

(i)

218.00 m
(ii)

173.00 m
(iii)

193.00 m
(iv)

214.00 m
(v)

200.00 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)

(

4
7

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

(i)

333.00 m
(ii)

292.00 m
(iii)

298.00 m
(iv)

337.00 m
(v)

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

(i)

200.00 m
(ii)

174.00 m
(iii)

207.00 m
(iv)

216.00 m
(v)

192.00 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)

(

15
8

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

(i)

400.00 m
(ii)

381.00 m
(iii)

375.00 m
(iv)

371.00 m
(v)

348.00 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)

(

4
3

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

(i)

85.00 m
(ii)

75.00 m
(iii)

83.00 m
(iv)

80.00 m
(v)

77.00 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)

(

3
8

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

(i)

406.00 m
(ii)

400.00 m
(iii)

372.00 m
(iv)

396.00 m
(v)

427.00 m

Question 16

16.

A
tower
stands vertically on the ground.

The distance between the observation point and its foot
tower
is
80

√

3

m
.

The distance between the observation point and its top
is
160

m
.

Find the angle of elevation.

(i)

60°
(ii)

90°
(iii)

45°
(iv)

30°
(v)

75°

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

(i)

281.82 m
(ii)

235.82 m
(iii)

259.82 m
(iv)

264.82 m
(v)

255.82 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 170 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)

98.15 m
(ii)

103.15 m
(iii)

101.15 m
(iv)

95.15 m
(v)

93.15 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)

6.45 m
(ii)

8.45 m
(iii)

7.45 m
(iv)

9.45 m
(v)

10.45 m

Question 20

20.

An observer 1.8 m tall, is 30 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)

22.12 m
(ii)

16.12 m
(iii)

24.12 m
(iv)

14.12 m
(v)

19.12 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 60° and 30° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

2.17 m

, distances away =

3.75 m

,

1.25 m
(ii)
height =

1.17 m

, distances away =

2.75 m

,

0.25 m
(iii)
height =

3.17 m

, distances away =

4.75 m

,

2.25 m
(iv)
height =

4.17 m

, distances away =

5.75 m

,

3.25 m
(v)
height =

0.17 m

, distances away =

1.75 m

,

9.25 m

Question 22

22.

From the top of a light house which is 90 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)

35.04 m
(ii)

38.04 m
(iii)

41.04 m
(iv)

33.04 m
(v)

43.04 m

Question 23

23.

From the top of a 19 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 30°. Find the height of the cable tower.

(i)

81.00 m
(ii)

73.00 m
(iii)

79.00 m
(iv)

76.00 m
(v)

71.00 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 60°. If the height of the tower is 85 m, find the height of the building .

(i)

25.33 m
(ii)

23.33 m
(iii)

33.33 m
(iv)

28.33 m
(v)

31.33 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 45° and the angle of elevation of the top of the building is 30°. If the height of the building is 16 m, find the height of the flag staff .

(i)

8.71 m
(ii)

6.71 m
(iii)

11.71 m
(iv)

16.71 m
(v)

14.71 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 20 m, find the height of the building .

(i)

5.00 m
(ii)

13.00 m
(iii)

15.00 m
(iv)

10.00 m
(v)

7.00 m

Assignment Key