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
cos
(-1)
(
1
2
)
.
If the distance between the point and the foot of the
tower
is
100 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
186.00 m
(ii)
213.00 m
(iii)
214.00 m
(iv)
200.00 m
(v)
182.00 m
Question
2
2.
The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 45°. If the height of the tower is 100 m, find the height of the building .
(i)
52.74 m
(ii)
62.74 m
(iii)
54.74 m
(iv)
57.74 m
(v)
60.74 m
Question
3
3.
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 58°7'. If the height of the radio tower is 11 m, find the distance between the observation point and the top of the radio tower.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
58
1.6003
1.6066
1.6128
1.6191
1.6255
1.6319
1.6383
1.6447
1.6512
1.6577
11
21
32
43
53
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
58
0.8450
0.8490
0.8499
0.8508
0.8517
0.8526
0.8536
0.8545
0.8554
0.8563
2
3
5
6
8
(i)
12.95 m
(ii)
9.95 m
(iii)
17.95 m
(iv)
15.95 m
(v)
7.95 m
Question
4
4.
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 40 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
101.57 m
(ii)
91.57 m
(iii)
99.57 m
(iv)
96.57 m
(v)
93.57 m
Question
5
5.
From a point 60 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 45° and 30° respectively. Find the height of the pillar.
(i)
22.36 m
(ii)
25.36 m
(iii)
28.36 m
(iv)
30.36 m
(v)
20.36 m
Question
6
6.
From the top of a 10 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)
22.32 m
(ii)
32.32 m
(iii)
27.32 m
(iv)
24.32 m
(v)
30.32 m
Question
7
7.
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 32°48'. If the distance between the observation point and the top of the tower is 16 m, find the height of the tower.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
32
0.5299
0.5314
0.5329
0.5344
0.5358
0.5373
0.5388
0.5402
0.5417
0.5432
2
5
7
10
12
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
32
0.8480
0.8471
0.8462
0.8453
0.8443
0.8434
0.8425
0.8415
0.8406
0.8393
2
3
5
6
8
(i)
9.67 m
(ii)
8.67 m
(iii)
6.67 m
(iv)
7.67 m
(v)
10.67 m
Question
8
8.
An observer 1.5 m tall, is 90 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)
169.39 m
(ii)
144.39 m
(iii)
157.39 m
(iv)
142.39 m
(v)
180.39 m
Question
9
9.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 140 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)
128.00 m
(ii)
155.00 m
(iii)
154.00 m
(iv)
140.00 m
(v)
112.00 m
Question
10
10.
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 50°58' and the angle of elevation of the top of the building is 21°50'. If the height of the flag staff is 9 m, find the height of the building .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
21
0.3839
0.3859
0.3879
0.3899
0.3919
0.3939
0.3959
0.3979
0.4000
0.4020
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'
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
(i)
2.33 m
(ii)
6.33 m
(iii)
4.33 m
(iv)
3.33 m
(v)
5.33 m
Question
11
11.
An observer 1.3 m tall, is 60 m away from a tower . The angle of elevation of the top of the tower from her eyes is 33°41'. 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)
44.29 m
(ii)
41.29 m
(iii)
38.29 m
(iv)
46.29 m
(v)
36.29 m
Question
12
12.
The angle of elevation of the top of a building from the foot of a tower is 41°5'. The angle of elevation of the top of the tower from the foot of the building is 37°22'. If the height of the tower is 75 m, find the height of the building .
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)
80.63 m
(ii)
88.63 m
(iii)
90.63 m
(iv)
85.63 m
(v)
82.63 m
Question
13
13.
The angles of depression of two boats from the top of a cliff 160 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
(i)
451.14 m
(ii)
419.14 m
(iii)
437.14 m
Question
14
14.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 50°38' 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'
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 Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
50
0.6428
0.6414
0.6401
0.6388
0.6374
0.6361
0.6347
0.6334
0.6320
0.6307
2
5
7
9
12
(i)
531.16 m
(ii)
555.16 m
(iii)
504.16 m
(iv)
543.16 m
(v)
524.16 m
Question
15
15.
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 45°36' and the angle of elevation of the top of the building is 26°13'. If the height of the building is 17 m, find the height of the flag staff .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
26
0.4877
0.4899
0.4921
0.4942
0.4964
0.4986
0.5008
0.5029
0.5051
0.5073
4
7
11
15
18
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
45
1.0000
1.0035
1.0070
1.0105
1.0141
1.0176
1.0212
1.0247
1.0283
1.0319
6
12
18
24
30
(i)
15.25 m
(ii)
18.25 m
(iii)
23.25 m
(iv)
13.25 m
(v)
21.25 m
Question
16
16.
From the top of a light house which is 60 m high from the sea level, the angles of depression of two ships are 33°35' and 27°5'. 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'
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
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
27
0.5095
0.5117
0.5139
0.5161
0.5184
0.5206
0.5228
0.5250
0.5272
0.5295
4
7
11
15
18
(i)
23.99 m
(ii)
21.99 m
(iii)
29.99 m
(iv)
26.99 m
(v)
31.99 m
Question
17
17.
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 47°23'. If the distance between the observation point and the top of the building is 19 m, find the distance between the observation point and the foot of the building.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
47
0.7314
0.7325
0.7337
0.7349
0.7361
0.7373
0.7385
0.7396
0.7408
0.7420
2
4
6
8
10
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
47
0.6820
0.6807
0.6794
0.6784
0.6769
0.6756
0.6743
0.6730
0.6717
0.6704
2
4
6
9
11
(i)
15.87 m
(ii)
12.87 m
(iii)
7.87 m
(iv)
17.87 m
(v)
9.87 m
Question
18
18.
From the top of a light house which is 55 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)
45.25 m
(ii)
35.25 m
(iii)
43.25 m
(iv)
40.25 m
(v)
37.25 m
Question
19
19.
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 20 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?
(i)
27 min 20 sec
(ii)
28 min 21 sec
(iii)
24 min 18 sec
(iv)
26 min 19 sec
(v)
30 min 22 sec
Question
20
20.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 10 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 37°10' and 55°56' respectively. Find the height of the other temple.
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
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
55
1.4281
1.4335
1.4388
1.4442
1.4496
1.4550
1.4605
1.4659
1.4715
1.4770
9
18
27
36
45
(i)
4.87 m
(ii)
2.87 m
(iii)
3.87 m
(iv)
5.87 m
(v)
6.87 m
Question
21
21.
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
200 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
200
m
(ii)
198
m
(iii)
201
m
(iv)
199
m
(v)
203
m
Question
22
22.
Two poles of equal height are standing opposite to each other on either side of a road which is 5 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 45° and 30° respectively. Find the height of each pole and the distances of the point from the two poles .
(i)
height =
0.83 m
, distances away =
2.17 m
,
0.83 m
(ii)
height =
3.83 m
, distances away =
5.17 m
,
3.83 m
(iii)
height =
9.83 m
, distances away =
1.17 m
,
9.83 m
(iv)
height =
1.83 m
, distances away =
3.17 m
,
1.83 m
(v)
height =
2.83 m
, distances away =
4.17 m
,
2.83 m
Question
23
23.
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 30° respectively. Find the height of the cliff.
(i)
43.19 m
(ii)
46.19 m
(iii)
41.19 m
(iv)
49.19 m
(v)
51.19 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
sec
(-1)
(
5
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)
28.33 m
(ii)
36.33 m
(iii)
30.33 m
(iv)
33.33 m
(v)
38.33 m
Question
25
25.
A man 1.4 m tall stands at a distance of 3.6 m from a lamp post and casts a shadow of 5.6 m on the ground. Find the height of the lamp post .
(i)
1.30 m
(ii)
2.30 m
(iii)
0.30 m
(iv)
3.30 m
(v)
4.30 m
Assignment Key
1) (iv)
2) (iv)
3) (i)
4) (iv)
5) (ii)
6) (iii)
7) (ii)
8) (iii)
9) (iv)
10) (iii)
11) (ii)
12) (iv)
13) (iii)
14) (i)
15) (ii)
16) (iv)
17) (ii)
18) (iv)
19) (i)
20) (i)
21) (i)
22) (iv)
23) (ii)
24) (iv)
25) (ii)
