EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Some Applications of Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
From the top of a 13 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)
47.00 m
(ii)
57.00 m
(iii)
49.00 m
(iv)
55.00 m
(v)
52.00 m
Question
2
2.
The shadow of a vertical tower BA on a level ground is increased by 15 m, when the altitude of the sun changes from 60° to 45°. Find the height of the tower .
(i)
38.49 m
(ii)
40.49 m
(iii)
30.49 m
(iv)
32.49 m
(v)
35.49 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 39°9'. If the height of the chimney is 5 m, find the distance between the observation point and the foot of the chimney.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
39
0.8098
0.8127
0.8156
0.8185
0.8214
0.8243
0.8273
0.8302
0.8332
0.8361
5
10
15
19
24
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
39
0.6293
0.6307
0.6320
0.6334
0.6347
0.6361
0.6374
0.6388
0.6401
0.6414
2
5
7
9
12
(i)
7.14 m
(ii)
8.14 m
(iii)
5.14 m
(iv)
4.14 m
(v)
6.14 m
Question
4
4.
Two vertical poles are on either side of a road. A 21 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 45° with the pole and when it is turned to rest against another pole, it makes an angle of 30° with the road. Find the width of the road.
(i)
28.04 m
(ii)
36.04 m
(iii)
33.04 m
(iv)
38.04 m
(v)
30.04 m
Question
5
5.
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 distance between the point and the top of the
tower
is
150 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
225
m
(ii)
75
√
3
m
(iii)
75
m
(iv)
75
√
18
m
(v)
225
2
√
2
m
Question
6
6.
A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards him. If it takes 7 min for the angle of depression to change from 45° to 60°, how soon after this, will the car reach the observation tower?
(i)
9 min 34 sec
(ii)
10 min 35 sec
(iii)
6 min 31 sec
(iv)
11 min 36 sec
(v)
8 min 33 sec
Question
7
7.
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 height of the
radio tower
is
160 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
240
√
2
m
(ii)
480
m
(iii)
160
m
(iv)
160
√
18
m
(v)
160
√
3
m
Question
8
8.
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 52°20'. If the distance between the observation point and the foot of the chimney is 5 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'
52
1.2799
1.2846
1.2892
1.2938
1.2985
1.3032
1.3079
1.3127
1.3175
1.3222
8
16
24
31
39
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
52
0.6157
0.6143
0.6129
0.6115
0.6101
0.6088
0.6074
0.6060
0.6046
0.6032
2
5
7
9
12
(i)
8.18 m
(ii)
7.18 m
(iii)
6.18 m
(iv)
10.18 m
(v)
9.18 m
Question
9
9.
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 80 m, find the height of the building .
(i)
46.19 m
(ii)
43.19 m
(iii)
41.19 m
(iv)
51.19 m
(v)
49.19 m
Question
10
10.
The angles of depression of two boats from the top of a cliff 200 m high are 30° and 45° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
(i)
531.42 m
(ii)
539.42 m
(iii)
546.42 m
(iv)
552.42 m
(v)
559.42 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)
(
5
7
)
.
If the distance between the point and the top of the
tower
is
150 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
107.14 m
(ii)
95.14 m
(iii)
103.14 m
(iv)
115.14 m
(v)
123.14 m
Question
12
12.
The angles of depression of two boats from the top of a cliff 160 m high are 30° and 45° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
(i)
135.14 m
(ii)
117.14 m
(iii)
122.14 m
(iv)
115.14 m
(v)
91.14 m
Question
13
13.
A man in a boat rowing away from a lighthouse 80 m high, takes 2 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.
(i)
0.28 m/sec
(ii)
2.28 m/sec
(iii)
8.28 m/sec
(iv)
1.28 m/sec
(v)
7.28 m/sec
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
cot
(-1)
(
5
7
)
.
If the height of the
tower
is
130 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
92.86 m
(ii)
95.86 m
(iii)
97.86 m
(iv)
87.86 m
(v)
89.86 m
Question
15
15.
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 10 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
21.14 m
(ii)
27.14 m
(iii)
19.14 m
(iv)
29.14 m
(v)
24.14 m
Question
16
16.
A boy standing on a vertical cliff in a jungle observes two rest houses in line with him on opposite sides deep in the jungle below. If their angles of depression are 45° and 60° and the distance between them is 190 m , find the height of the cliff.
(i)
137.46 m
(ii)
102.46 m
(iii)
120.46 m
(iv)
106.46 m
(v)
136.46 m
Question
17
17.
A
tower
stands vertically on the ground.
The distance between the observation point and its foot
tower
is
80
√
2
m
.
The distance between the observation point and its top
is
160
m
.
Find the angle of elevation.
(i)
105°
(ii)
60°
(iii)
30°
(iv)
75°
(v)
45°
Question
18
18.
An observer 1.3 m tall, is 10 m away from a tower . The angle of elevation of the top of the tower from her eyes is 33°19'. Find the height of the tower .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
33
0.6494
0.6519
0.6544
0.6569
0.6594
0.6619
0.6644
0.6669
0.6694
0.6720
4
8
13
17
21
(i)
6.87 m
(ii)
8.87 m
(iii)
9.87 m
(iv)
5.87 m
(v)
7.87 m
Question
19
19.
From the top of a light house which is 60 m high from the sea level, the angles of depression of two ships are 48°54' and 32°15'. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
48
1.1106
1.1145
1.1184
1.1224
1.1263
1.1303
1.1343
1.1383
1.1423
1.1463
7
13
20
27
33
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
32
0.6249
0.6273
0.6297
0.6322
0.6346
0.6371
0.6395
0.6420
0.6445
0.6469
4
8
12
17
21
(i)
39.76 m
(ii)
42.76 m
(iii)
45.76 m
(iv)
47.76 m
(v)
37.76 m
Question
20
20.
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
21
21.
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 foot of the
building
is
140 m
,
find the height of the
building
.
(i)
140
m
(ii)
141
m
(iii)
137
m
(iv)
142
m
(v)
139
m
Question
22
22.
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 51°11'. If the distance between the observation point and the top of the radio tower is 5 m, find the distance between the observation point and the foot of the radio tower.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
51
0.7771
0.7782
0.7793
0.7804
0.7815
0.7826
0.7837
0.7848
0.7859
0.7869
2
4
5
7
9
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
51
0.6293
0.6280
0.6266
0.6252
0.6239
0.6225
0.6211
0.6198
0.6184
0.9170
2
5
7
9
12
(i)
5.13 m
(ii)
3.13 m
(iii)
4.13 m
(iv)
2.13 m
(v)
1.13 m
Question
23
23.
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 41°51' and 37°29' respectively. Find the height of each pole and the distances of the point from the two poles .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
41
0.8693
0.8724
0.8754
0.8785
0.8816
0.8847
0.8878
0.8910
0.8941
0.8972
5
10
16
21
26
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
37
0.7536
0.7563
0.7590
0.7618
0.7646
0.7673
0.7701
0.7729
0.7757
0.7785
5
9
14
19
23
(i)
height =
6.13 m
, distances away =
7.39 m
,
6.61 m
(ii)
height =
2.13 m
, distances away =
3.39 m
,
2.61 m
(iii)
height =
4.13 m
, distances away =
5.39 m
,
4.61 m
(iv)
height =
5.13 m
, distances away =
6.39 m
,
5.61 m
(v)
height =
3.13 m
, distances away =
4.39 m
,
3.61 m
Question
24
24.
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)
(
11
7
)
.
If the distance between the point and the top of the
tower
is
170 m
,
find the height of the
tower
.
(i)
125.18 m
(ii)
100.18 m
(iii)
96.18 m
(iv)
112.18 m
(v)
108.18 m
Question
25
25.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 35°33' with the ground. The top of the tree touches the ground at a distance of 120 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'
35
0.7002
0.7028
0.7054
0.7080
0.7107
0.7133
0.7159
0.7186
0.7212
0.7239
4
9
13
17
22
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
35
0.8192
0.8181
0.8171
0.8161
0.8151
0.8141
0.8131
0.8121
0.8111
0.8100
2
3
5
7
8
(i)
238.24 m
(ii)
217.24 m
(iii)
233.24 m
(iv)
220.24 m
(v)
246.24 m
Assignment Key
1) (v)
2) (v)
3) (v)
4) (iii)
5) (ii)
6) (i)
7) (v)
8) (i)
9) (i)
10) (iii)
11) (i)
12) (ii)
13) (i)
14) (i)
15) (v)
16) (iii)
17) (v)
18) (v)
19) (ii)
20) (i)
21) (i)
22) (ii)
23) (iii)
24) (v)
25) (iii)
