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
45°
.
If the height of the
chimney
is
200 m
,
find the distance between
the observation point and the top of the
chimney
.
(i)
400
√
3
m
(ii)
200
√
2
m
(iii)
100
√
12
m
(iv)
200
m
(v)
400
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
10 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
11
m
(ii)
9
m
(iii)
12
m
(iv)
10
m
(v)
7
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
70 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
140
m
(ii)
70
m
(iii)
140
√
3
m
(iv)
70
√
2
m
(v)
35
√
12
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
170 m
,
find the height of the
building
.
(i)
170
m
(ii)
170
3
√
18
m
(iii)
170
3
√
3
m
(iv)
170
3
m
(v)
85
√
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
70 m
,
find the height of the
building
.
(i)
35
√
3
m
(ii)
105
2
√
2
m
(iii)
35
m
(iv)
105
m
(v)
35
√
18
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
60°
.
If the distance between the point and the top of the
tower
is
100 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
51
m
(ii)
47
m
(iii)
49
m
(iv)
50
m
(v)
52
m
Question
7
7.
A
tower
stands vertically on the ground.
The distance between the observation point and its foot
tower
is
30
m
.
The distance between the observation point and its top
is
60
m
.
Find the angle of elevation.
(i)
30°
(ii)
105°
(iii)
45°
(iv)
90°
(v)
60°
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)
39.64 m
(ii)
29.64 m
(iii)
34.64 m
(iv)
31.64 m
(v)
37.64 m
Question
9
9.
An observer 1.9 m tall, is 100 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)
85.90 m
(ii)
129.90 m
(iii)
116.90 m
(iv)
101.90 m
(v)
88.90 m
Question
10
10.
A man 1.3 m tall stands at a distance of 3.6 m from a lamp post and casts a shadow of 3.2 m on the ground. Find the height of the lamp post .
(i)
1.76 m
(ii)
2.76 m
(iii)
0.76 m
(iv)
4.76 m
(v)
3.76 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)
∠c
(iii)
∠f
(iv)
∠e
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)
∠b
(ii)
∠d
(iii)
∠a
(iv)
∠c
Assignment Key
1) (ii)
2) (iv)
3) (iv)
4) (iii)
5) (i)
6) (iv)
7) (v)
8) (iii)
9) (iv)
10) (ii)
11) (ii)
12) (iv)
