EduSahara™ Assignment
Name : Heights and Distances1
Chapter : Applications of Trigonometry
Grade : SSC Grade X
License : Non Commercial Use
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
100 m
,
find the distance between
the observation point and the top of the
radio tower
.
(i)
200
3
√
18
m
(ii)
100
√
2
m
(iii)
200
3
√
3
m
(iv)
200
m
(v)
200
3
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
45°
.
If the height of the
chimney
is
70 m
,
find the distance between
the observation point and the foot of the
chimney
.
(i)
70
m
(ii)
69
m
(iii)
73
m
(iv)
67
m
(v)
71
m
Question
3
3.
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
45°
.
If the distance between the point and the foot of the
radio tower
is
40 m
,
find the distance between
the observation point and the top of the
radio tower
.
(i)
80
√
3
m
(ii)
20
√
12
m
(iii)
40
√
2
m
(iv)
80
m
(v)
40
m
Question
4
4.
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
70 m
,
find the height of the
tower
.
(i)
72
m
(ii)
69
m
(iii)
70
m
(iv)
71
m
(v)
68
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
30°
.
If the distance between the point and the top of the
building
is
10 m
,
find the height of the
building
.
(i)
5
m
(ii)
4
m
(iii)
8
m
(iv)
6
m
(v)
2
m
Question
6
6.
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 distance between the point and the top of the
tower
is
140 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
105
√
2
m
(ii)
70
√
3
m
(iii)
70
m
(iv)
210
m
(v)
70
√
18
m
Question
7
7.
A
tower
stands vertically on the ground.
The height of the
tower
is
110
m
.
The distance between the observation point and its top
is
220
m
.
Find the angle of elevation.
(i)
90°
(ii)
45°
(iii)
75°
(iv)
30°
(v)
60°
Question
8
8.
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 60 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
148.85 m
(ii)
144.85 m
(iii)
166.85 m
(iv)
141.85 m
(v)
128.85 m
Question
9
9.
An observer 1.8 m tall, is 50 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)
85.41 m
(ii)
93.41 m
(iii)
88.41 m
(iv)
91.41 m
(v)
83.41 m
Question
10
10.
A man 1.9 m tall stands at a distance of 3.8 m from a lamp post and casts a shadow of 9.1 m on the ground. Find the height of the lamp post .
(i)
2.69 m
(ii)
3.69 m
(iii)
1.69 m
(iv)
0.69 m
(v)
4.69 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)
∠e
(ii)
∠c
(iii)
∠d
(iv)
∠b
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)
∠f
(ii)
∠e
(iii)
∠c
(iv)
∠d
Assignment Key
1) (iii)
2) (i)
3) (iii)
4) (iii)
5) (i)
6) (ii)
7) (iv)
8) (ii)
9) (iii)
10) (i)
11) (iv)
12) (ii)
