EduSahara™ Assignment
Name : Heights and Distances1
Chapter : Applications of Trigonometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
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
150 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
303
m
(ii)
301
m
(iii)
297
m
(iv)
300
m
(v)
299
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
50 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
50
√
18
m
(ii)
50
√
3
m
(iii)
150
m
(iv)
75
√
2
m
(v)
50
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
30°
.
If the distance between the point and the foot of the
radio tower
is
20 m
,
find the distance between
the observation point and the top of the
radio tower
.
(i)
40
m
(ii)
20
√
2
m
(iii)
40
3
√
18
m
(iv)
40
3
√
3
m
(v)
40
3
m
Question
4
4.
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 distance between the point and the foot of the
radio tower
is
180 m
,
find the height of the
radio tower
.
(i)
180
√
3
m
(ii)
540
m
(iii)
180
m
(iv)
180
√
18
m
(v)
270
√
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
45°
.
If the distance between the point and the top of the
building
is
30 m
,
find the height of the
building
.
(i)
30
m
(ii)
15
m
(iii)
15
2
√
12
m
(iv)
30
√
3
m
(v)
15
√
2
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
60°
.
If the distance between the point and the top of the
radio tower
is
90 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
45
m
(ii)
46
m
(iii)
48
m
(iv)
43
m
(v)
44
m
Question
7
7.
A
tower
stands vertically on the ground.
The distance between the observation point and its foot
tower
is
50
√
2
m
.
The distance between the observation point and its top
is
100
m
.
Find the angle of elevation.
(i)
105°
(ii)
45°
(iii)
30°
(iv)
60°
(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 40 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
74.29 m
(ii)
64.29 m
(iii)
66.29 m
(iv)
72.29 m
(v)
69.29 m
Question
9
9.
An observer 1.4 m tall, is 150 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)
151.40 m
(ii)
173.40 m
(iii)
138.40 m
(iv)
147.40 m
(v)
153.40 m
Question
10
10.
A man 1.6 m tall stands at a distance of 8.7 m from a lamp post and casts a shadow of 7.1 m on the ground. Find the height of the lamp post .
(i)
2.56 m
(ii)
4.56 m
(iii)
3.56 m
(iv)
1.56 m
(v)
5.56 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)
∠b
(iii)
∠e
(iv)
∠c
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)
∠d
(iii)
∠e
(iv)
∠b
Assignment Key
1) (iv)
2) (ii)
3) (iv)
4) (i)
5) (v)
6) (i)
7) (ii)
8) (v)
9) (i)
10) (iii)
11) (ii)
12) (ii)
