EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Some Applications of Trigonometry
Grade : CBSE 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
tan
(-1)
(
1
5
)
.
If the distance between the point and the foot of the
tower
is
160 m
,
find the height of the
tower
.
(i)
37.00 m
(ii)
27.00 m
(iii)
29.00 m
(iv)
32.00 m
(v)
35.00 m
Question
2
2.
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)
29.64 m
(iv)
37.64 m
(v)
39.64 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 59°48'. If the distance between the observation point and the foot of the chimney is 14 m, find the height of the chimney.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
59
1.6643
1.6709
1.6775
1.6842
1.6909
1.6977
1.7045
1.7113
1.7182
1.7251
11
23
34
45
56
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
59
0.5151
0.5135
0.5120
0.5105
0.5090
0.5075
0.5080
0.5045
0.5030
0.5015
3
5
8
10
13
(i)
24.05 m
(ii)
27.05 m
(iii)
19.05 m
(iv)
29.05 m
(v)
21.05 m
Question
4
4.
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)
30°
(ii)
45°
(iii)
105°
(iv)
60°
(v)
75°
Question
5
5.
Two vertical poles are on either side of a road. A 29 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 60° with the pole and when it is turned to rest against another pole, it makes an angle of 45° with the road. Find the width of the road.
(i)
40.01 m
(ii)
30.01 m
(iii)
38.01 m
(iv)
35.01 m
(v)
32.01 m
Question
6
6.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 40°27' with the ground. The top of the tree touches the ground at a distance of 190 m from the foot of the tree . Find the height of the tree before it was broken.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
40
0.8391
0.8421
0.8451
0.8481
0.8511
0.8541
0.8571
0.8601
0.8632
0.8662
5
10
15
20
25
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
40
0.7660
0.7649
0.7638
0.7627
0.7615
0.7604
0.7593
0.7581
0.7570
0.7559
2
4
6
7
9
(i)
429.70 m
(ii)
409.70 m
(iii)
396.70 m
(iv)
418.70 m
(v)
411.70 m
Question
7
7.
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 50°13'. If the height of the chimney is 9 m, find the distance between the observation point and the top of the chimney.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
50
1.1918
1.1960
1.2002
1.2045
1.2088
1.2131
1.2174
1.2218
1.2261
1.2305
7
14
22
29
36
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
50
0.7660
0.7672
0.7683
0.7694
0.7705
0.7716
0.7727
0.7738
0.7749
0.7760
2
4
6
7
9
(i)
14.71 m
(ii)
11.71 m
(iii)
8.71 m
(iv)
16.71 m
(v)
6.71 m
Question
8
8.
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 height of the
tower
is
110 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
976.00 m
(ii)
997.00 m
(iii)
1004.00 m
(iv)
978.00 m
(v)
990.00 m
Question
9
9.
A person, walking 50 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)
75
2
√
2
m
(ii)
25
√
18
m
(iii)
75
m
(iv)
25
m
(v)
25
√
3
m
Question
10
10.
Two poles of equal height are standing opposite to each other on either side of a road which is 15 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 45° respectively. Find the height of each pole and the distances of the point from the two poles .
(i)
height =
8.51 m
, distances away =
8.51 m
,
4.49 m
(ii)
height =
10.51 m
, distances away =
10.51 m
,
6.49 m
(iii)
height =
7.51 m
, distances away =
7.51 m
,
3.49 m
(iv)
height =
11.51 m
, distances away =
11.51 m
,
7.49 m
(v)
height =
9.51 m
, distances away =
9.51 m
,
5.49 m
Question
11
11.
An observer 1.7 m tall, is 130 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)
137.70 m
(ii)
126.70 m
(iii)
131.70 m
(iv)
103.70 m
(v)
149.70 m
Question
12
12.
An aeroplane is flying horizontally 1600 m above the ground. From a point of observation, which lies exactly below the path of the aeroplane, the angle of elevation at a certain instant is 38°. After 10 sec , its elevation from the same point changes to 22°. Find the uniform speed of the aeroplane .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
22
0.4040
0.4061
0.4081
0.4101
0.4122
0.4142
0.4163
0.4183
0.4202
0.4224
3
7
10
13
17
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
38
0.7813
0.7841
0.7869
0.7898
0.7926
0.7954
0.7983
0.8012
0.8040
0.8069
5
9
14
19
23
(i)
691.51 kmph
(ii)
688.51 kmph
(iii)
712.51 kmph
(iv)
675.51 kmph
(v)
676.51 kmph
Question
13
13.
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
200 m
,
find the height of the
chimney
.
(i)
200
m
(ii)
200
3
√
18
m
(iii)
200
3
√
3
m
(iv)
200
3
m
(v)
100
√
2
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
cosec
(-1)
(
4
3
)
.
If the height of the
tower
is
30 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
35.00 m
(ii)
37.00 m
(iii)
40.00 m
(iv)
43.00 m
(v)
45.00 m
Question
15
15.
From a point 80 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 45° respectively. Find the height of the pillar.
(i)
55.57 m
(ii)
53.57 m
(iii)
61.57 m
(iv)
63.57 m
(v)
58.57 m
Question
16
16.
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)
∠a
(ii)
∠d
(iii)
∠b
(iv)
∠c
Question
17
17.
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 10 m, find the height of the flag staff .
(i)
5.32 m
(ii)
8.32 m
(iii)
6.32 m
(iv)
7.32 m
(v)
9.32 m
Question
18
18.
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
3
)
.
If the distance between the point and the foot of the
tower
is
160 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
480.00 m
(ii)
474.00 m
(iii)
492.00 m
(iv)
462.00 m
(v)
493.00 m
Question
19
19.
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 top of the
chimney
is
190 m
,
find the height of the
chimney
.
(i)
93
m
(ii)
94
m
(iii)
96
m
(iv)
98
m
(v)
95
m
Question
20
20.
From the top of a 14 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 45°. Find the height of the cable tower.
(i)
43.25 m
(ii)
41.25 m
(iii)
35.25 m
(iv)
33.25 m
(v)
38.25 m
Question
21
21.
From the top of a 13 m high building , the angle of elevation of the top of a cable tower is 47°36' and the angle of depression of its foot is 25°38'. Find the height of the cable tower.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
47
1.0724
1.0761
1.0799
1.0837
1.0875
1.0913
1.0951
1.0990
1.1028
1.1067
6
13
19
25
32
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
25
0.4663
0.4684
0.4706
0.4727
0.4748
0.4770
0.4791
0.4813
0.4834
0.4856
4
7
11
14
18
(i)
47.67 m
(ii)
42.67 m
(iii)
45.67 m
(iv)
37.67 m
(v)
39.67 m
Question
22
22.
The angles of depression of two boats from the top of a cliff 120 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
(i)
82.85 m
(ii)
84.85 m
(iii)
90.85 m
(iv)
87.85 m
(v)
92.85 m
Question
23
23.
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 30° and 45° respectively. Find the height of the other temple.
(i)
62.62 m
(ii)
67.62 m
(iii)
64.62 m
(iv)
70.62 m
(v)
72.62 m
Question
24
24.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 200 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 45° respectively. Find the width of the river .
(i)
212.00 m
(ii)
193.00 m
(iii)
200.00 m
(iv)
224.00 m
(v)
173.00 m
Question
25
25.
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
180 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
90
√
2
m
(ii)
90
m
(iii)
180
m
(iv)
45
√
12
m
(v)
180
√
3
m
Assignment Key
1) (iv)
2) (ii)
3) (i)
4) (ii)
5) (iv)
6) (v)
7) (ii)
8) (v)
9) (v)
10) (v)
11) (iii)
12) (ii)
13) (iii)
14) (iii)
15) (v)
16) (i)
17) (iv)
18) (i)
19) (v)
20) (v)
21) (ii)
22) (iv)
23) (ii)
24) (iii)
25) (i)
