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
180 m
,
find the distance between
the observation point and the top of the
chimney
.
(i)
361
m
(ii)
360
m
(iii)
362
m
(iv)
358
m
(v)
359
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
45°
.
If the height of the
radio tower
is
170 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
170
m
(ii)
169
m
(iii)
173
m
(iv)
171
m
(v)
168
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
100 m
,
find the distance between
the observation point and the top of the
radio tower
.
(i)
50
√
12
m
(ii)
100
m
(iii)
200
m
(iv)
100
√
2
m
(v)
200
√
3
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
60°
.
If the distance between the point and the foot of the
building
is
20 m
,
find the height of the
building
.
(i)
20
m
(ii)
20
√
18
m
(iii)
60
m
(iv)
20
√
3
m
(v)
30
√
2
m
Question
5
5.
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
70 m
,
find the height of the
radio tower
.
(i)
37
m
(ii)
32
m
(iii)
36
m
(iv)
34
m
(v)
35
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
60°
.
If the distance between the point and the top of the
building
is
130 m
,
find the distance between
the observation point and the foot of the
building
.
(i)
64
m
(ii)
67
m
(iii)
62
m
(iv)
65
m
(v)
66
m
Question
7
7.
A
tower
stands vertically on the ground.
The height of the
tower
is
200
m
.
The distance between the observation point and its foot
is
200
m
.
Find the angle of elevation.
(i)
105°
(ii)
30°
(iii)
60°
(iv)
45°
(v)
75°
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)
31.64 m
(ii)
34.64 m
(iii)
39.64 m
(iv)
29.64 m
(v)
37.64 m
Question
9
9.
An observer 1.9 m tall, is 170 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)
296.36 m
(ii)
313.36 m
(iii)
270.36 m
(iv)
293.36 m
(v)
308.36 m
Question
10
10.
A man 1.7 m tall stands at a distance of 5.3 m from a lamp post and casts a shadow of 2.3 m on the ground. Find the height of the lamp post .
(i)
6.62 m
(ii)
5.62 m
(iii)
4.62 m
(iv)
7.62 m
(v)
3.62 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)
∠g
(iii)
∠f
(iv)
∠d
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)
∠d
(ii)
∠e
(iii)
∠b
(iv)
∠c
Assignment Key
1) (ii)
2) (i)
3) (iv)
4) (iv)
5) (v)
6) (iv)
7) (iv)
8) (ii)
9) (i)
10) (ii)
11) (iv)
12) (i)
