EduSahara™ Assignment
Name : Heights and Distances1
Chapter : Applications of Trigonometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
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 height of the
building
is
20 m
,
find the distance between
the observation point and the top of the
building
.
(i)
40
3
m
(ii)
40
3
√
3
m
(iii)
40
m
(iv)
40
3
√
18
m
(v)
20
√
2
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
160 m
,
find the distance between
the observation point and the foot of the
chimney
.
(i)
160
m
(ii)
161
m
(iii)
159
m
(iv)
162
m
(v)
158
m
Question
3
3.
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 distance between the point and the foot of the
chimney
is
170 m
,
find the distance between
the observation point and the top of the
chimney
.
(i)
340
m
(ii)
170
√
2
m
(iii)
340
3
m
(iv)
340
3
√
18
m
(v)
340
3
√
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
60 m
,
find the height of the
building
.
(i)
180
m
(ii)
60
√
3
m
(iii)
90
√
2
m
(iv)
60
m
(v)
60
√
18
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
60 m
,
find the height of the
building
.
(i)
31
m
(ii)
32
m
(iii)
30
m
(iv)
29
m
(v)
27
m
Question
6
6.
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 distance between the point and the top of the
chimney
is
80 m
,
find the distance between
the observation point and the foot of the
chimney
.
(i)
20
√
12
m
(ii)
40
m
(iii)
80
√
3
m
(iv)
40
√
2
m
(v)
80
m
Question
7
7.
A
tower
stands vertically on the ground.
The distance between the observation point and its foot
tower
is
150
m
.
The distance between the observation point and its top
is
300
m
.
Find the angle of elevation.
(i)
105°
(ii)
45°
(iii)
90°
(iv)
60°
(v)
30°
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 90 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
243.28 m
(ii)
219.28 m
(iii)
217.28 m
(iv)
202.28 m
(v)
205.28 m
Question
9
9.
An observer 1.8 m tall, is 140 m away from a tower . The angle of elevation of the top of the tower from her eyes is 30°. Find the height of the tower .
(i)
79.64 m
(ii)
82.64 m
(iii)
85.64 m
(iv)
87.64 m
(v)
77.64 m
Question
10
10.
A man 1.6 m tall stands at a distance of 1.4 m from a lamp post and casts a shadow of 3.4 m on the ground. Find the height of the lamp post .
(i)
0.26 m
(ii)
3.26 m
(iii)
4.26 m
(iv)
1.26 m
(v)
2.26 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)
∠d
(iii)
∠f
(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)
∠d
(ii)
∠c
(iii)
∠e
(iv)
∠b
Assignment Key
1) (ii)
2) (i)
3) (v)
4) (ii)
5) (iii)
6) (iv)
7) (iv)
8) (iii)
9) (ii)
10) (v)
11) (iv)
12) (i)
