EduSahara™ Assignment
Name : Heights and Distances1
Chapter : Applications of Trigonometry
Grade : SSC Grade X
License : Non Commercial Use
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
30°
.
If the height of the
chimney
is
30 m
,
find the distance between
the observation point and the top of the
chimney
.
(i)
60
m
(ii)
59
m
(iii)
61
m
(iv)
57
m
(v)
62
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
160 m
,
find the distance between
the observation point and the foot of the
building
.
(i)
160
√
18
m
(ii)
480
m
(iii)
240
√
2
m
(iv)
160
m
(v)
160
√
3
m
Question
3
3.
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 foot of the
building
is
20 m
,
find the distance between
the observation point and the top of the
building
.
(i)
42
m
(ii)
39
m
(iii)
37
m
(iv)
41
m
(v)
40
m
Question
4
4.
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 foot of the
building
is
110 m
,
find the height of the
building
.
(i)
110
3
√
18
m
(ii)
110
m
(iii)
110
3
√
3
m
(iv)
55
√
2
m
(v)
110
3
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
10 m
,
find the height of the
tower
.
(i)
15
2
√
2
m
(ii)
5
√
18
m
(iii)
5
√
3
m
(iv)
5
m
(v)
15
m
Question
6
6.
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 distance between the point and the top of the
radio tower
is
160 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
80
√
18
m
(ii)
120
√
2
m
(iii)
240
m
(iv)
80
m
(v)
80
√
3
m
Question
7
7.
A
tower
stands vertically on the ground.
The distance between the observation point and its foot
tower
is
120
√
2
m
.
The distance between the observation point and its top
is
240
m
.
Find the angle of elevation.
(i)
105°
(ii)
30°
(iii)
75°
(iv)
60°
(v)
45°
Question
8
8.
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 20 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
34.64 m
(ii)
29.64 m
(iii)
39.64 m
(iv)
37.64 m
(v)
31.64 m
Question
9
9.
An observer 1.7 m tall, is 20 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)
26.70 m
(ii)
24.70 m
(iii)
18.70 m
(iv)
21.70 m
(v)
16.70 m
Question
10
10.
A man 1.4 m tall stands at a distance of 4.4 m from a lamp post and casts a shadow of 8.5 m on the ground. Find the height of the lamp post .
(i)
3.12 m
(ii)
1.12 m
(iii)
4.12 m
(iv)
0.12 m
(v)
2.12 m
Question
11
11.
If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?
(i)
∠d
(ii)
∠g
(iii)
∠e
(iv)
∠f
Question
12
12.
If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?
(i)
∠c
(ii)
∠e
(iii)
∠d
(iv)
∠b
Assignment Key
1) (i)
2) (v)
3) (v)
4) (iii)
5) (iii)
6) (v)
7) (v)
8) (i)
9) (iv)
10) (v)
11) (i)
12) (iii)
