EduSahara™ Assignment
Name : Heights and Distances
Chapter : Some Applications of Trigonometry
Grade : CBSE 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
30°
.
If the height of the
building
is
80 m
,
find the distance between
the observation point and the top of the
building
.
(i)
160
m
(ii)
162
m
(iii)
159
m
(iv)
161
m
(v)
157
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
30°
.
If the height of the
chimney
is
20 m
,
find the distance between
the observation point and the foot of the
chimney
.
(i)
20
√
18
m
(ii)
20
√
3
m
(iii)
20
m
(iv)
30
√
2
m
(v)
60
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
60°
.
If the distance between the point and the foot of the
tower
is
30 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
59
m
(ii)
60
m
(iii)
58
m
(iv)
61
m
(v)
62
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
70 m
,
find the height of the
radio tower
.
(i)
105
√
2
m
(ii)
70
√
18
m
(iii)
70
√
3
m
(iv)
70
m
(v)
210
m
Question
5
5.
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
50 m
,
find the height of the
chimney
.
(i)
25
m
(ii)
25
2
√
12
m
(iii)
50
√
3
m
(iv)
25
√
2
m
(v)
50
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
45°
.
If the distance between the point and the top of the
radio tower
is
120 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
120
m
(ii)
30
√
12
m
(iii)
60
√
2
m
(iv)
120
√
3
m
(v)
60
m
Question
7
7.
Two boys are on opposite sides of a tower of 30 m height. They measure the angle of elevation of the top of the tower as 60° and 45° respectively. Find the distance between the two boys.
(i)
(
10
√
18
+
30
√
6
)
m
(ii)
(
−
2
−
√
3
)
m
(iii)
(
−
600
)
m
(iv)
(
15
√
2
+
15
√
6
)
m
(v)
(
10
√
3
+
30
)
m
Question
8
8.
A person, walking 35 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 60°. Find the height of the flagpost .
(i)
35
2
√
3
m
(ii)
35
2
m
(iii)
35
2
√
18
m
(iv)
105
2
m
(v)
105
4
√
2
m
Question
9
9.
A flagstaff stands on the top of a building at a distance of 30 m away from the foot of building . The angle of elevation of the top of the flagstaff is 45° and the angle of elevation of the top of the building is 30°. Find the height of the flagstaff .
(i)
(
30
√
6
−
10
√
18
)
m
(ii)
600
m
(iii)
(
30
−
10
√
3
)
m
(iv)
(
2
−
√
3
)
m
(v)
(
15
√
6
−
15
√
2
)
m
Question
10
10.
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
sin
(-1)
(
1
9
)
.
If the distance between the point and the top of the
tower
is
150 m
,
find the height of the
tower
.
(i)
21.67 m
(ii)
11.67 m
(iii)
13.67 m
(iv)
16.67 m
(v)
19.67 m
Question
11
11.
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
cos
(-1)
(
1
2
)
.
If the distance between the point and the foot of the
tower
is
180 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
375.00 m
(ii)
360.00 m
(iii)
357.00 m
(iv)
346.00 m
(v)
376.00 m
Question
12
12.
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
tan
(-1)
(
2
3
)
.
If the height of the
tower
is
130 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
212.00 m
(ii)
183.00 m
(iii)
195.00 m
(iv)
181.00 m
(v)
200.00 m
Question
13
13.
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
cosec
(-1)
(
4
3
)
.
If the height of the
tower
is
50 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
66.67 m
(ii)
61.67 m
(iii)
63.67 m
(iv)
71.67 m
(v)
69.67 m
Question
14
14.
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
sec
(-1)
(
4
3
)
.
If the distance between the point and the foot of the
tower
is
20 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
26.67 m
(ii)
23.67 m
(iii)
21.67 m
(iv)
31.67 m
(v)
29.67 m
Question
15
15.
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
cot
(-1)
(
2
5
)
.
If the distance between the point and the foot of the
tower
is
100 m
,
find the height of the
tower
.
(i)
254.00 m
(ii)
233.00 m
(iii)
267.00 m
(iv)
225.00 m
(v)
250.00 m
Question
16
16.
A
tower
stands vertically on the ground.
The height of the
tower
is
80
√
2
m
.
The distance between the observation point and its top
is
160
m
.
Find the angle of elevation.
(i)
45°
(ii)
60°
(iii)
105°
(iv)
75°
(v)
30°
Question
17
17.
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 130 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
309.85 m
(ii)
318.85 m
(iii)
296.85 m
(iv)
313.85 m
(v)
329.85 m
Question
18
18.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 60 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 60° respectively. Find the width of the river .
(i)
31.64 m
(ii)
39.64 m
(iii)
29.64 m
(iv)
34.64 m
(v)
37.64 m
Question
19
19.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 160 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 45° and 60° respectively. Find the height of the other temple.
(i)
64.63 m
(ii)
72.63 m
(iii)
70.63 m
(iv)
67.63 m
(v)
62.63 m
Question
20
20.
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)
310.36 m
(ii)
281.36 m
(iii)
272.36 m
(iv)
296.36 m
(v)
299.36 m
Question
21
21.
Two poles of equal height are standing opposite to each other on either side of a road which is 10 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of each pole and the distances of the point from the two poles .
(i)
height =
6.33 m
, distances away =
9.5 m
,
4.5 m
(ii)
height =
2.33 m
, distances away =
5.5 m
,
0.5 m
(iii)
height =
5.33 m
, distances away =
8.5 m
,
3.5 m
(iv)
height =
4.33 m
, distances away =
7.5 m
,
2.5 m
(v)
height =
3.33 m
, distances away =
6.5 m
,
1.5 m
Question
22
22.
From the top of a light house which is 80 m high from the sea level, the angles of depression of two ships are 45° and 30°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
(i)
63.55 m
(ii)
53.55 m
(iii)
61.55 m
(iv)
58.55 m
(v)
55.55 m
Question
23
23.
From the top of a 20 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Find the height of the cable tower.
(i)
75.00 m
(ii)
77.00 m
(iii)
80.00 m
(iv)
83.00 m
(v)
85.00 m
Question
24
24.
The angle of elevation of the top of a building from the foot of a tower is 45°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 65 m, find the height of the building .
(i)
34.53 m
(ii)
42.53 m
(iii)
40.53 m
(iv)
32.53 m
(v)
37.53 m
Question
25
25.
A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 45°. If the height of the building is 18 m, find the height of the flag staff .
(i)
13.18 m
(ii)
10.18 m
(iii)
18.18 m
(iv)
16.18 m
(v)
8.18 m
Question
26
26.
A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 5 m, find the height of the building .
(i)
0.50 m
(ii)
3.50 m
(iii)
4.50 m
(iv)
2.50 m
(v)
1.50 m
Assignment Key
1) (i)
2) (ii)
3) (ii)
4) (iii)
5) (iv)
6) (iii)
7) (v)
8) (i)
9) (iii)
10) (iv)
11) (ii)
12) (iii)
13) (i)
14) (i)
15) (v)
16) (i)
17) (iv)
18) (iv)
19) (iv)
20) (iv)
21) (iv)
22) (iv)
23) (iii)
24) (v)
25) (i)
26) (iv)
