EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Some Applications of Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
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 foot of the
chimney
is
40 m
,
find the distance between
the observation point and the top of the
chimney
.
(i)
80
√
3
m
(ii)
40
√
2
m
(iii)
80
m
(iv)
40
m
(v)
20
√
12
m
Question
2
2.
A person, walking 25 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 45°. Find the height of the flagpost .
(i)
625
2
m
(ii)
(
25
2
√
3
+
25
2
)
m
(iii)
(
2
+
√
3
)
m
(iv)
(
75
4
√
2
+
25
4
√
6
)
m
(v)
(
25
2
√
18
+
25
2
√
6
)
m
Question
3
3.
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 building is 7 m, find the height of the flag staff .
(i)
11.00 m
(ii)
17.00 m
(iii)
14.00 m
(iv)
19.00 m
(v)
9.00 m
Question
4
4.
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°16'. If the height of the tower is 6 m, find the distance between the observation point and the foot of the tower.
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
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
(i)
9.50 m
(ii)
10.50 m
(iii)
11.50 m
(iv)
8.50 m
(v)
7.50 m
Question
5
5.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 170 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 height of the other temple.
(i)
130.33 m
(ii)
97.33 m
(iii)
115.33 m
(iv)
113.33 m
(v)
105.33 m
Question
6
6.
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)
(
5
4
)
.
If the distance between the point and the top of the
tower
is
60 m
,
find the height of the
tower
.
(i)
48.00 m
(ii)
53.00 m
(iii)
51.00 m
(iv)
45.00 m
(v)
43.00 m
Question
7
7.
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 40°31' and the angle of elevation of the top of the building is 20°26'. If the height of the building is 18 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'
20
0.3640
0.3659
0.3679
0.3699
0.3719
0.3739
0.3759
0.3779
0.3799
0.3819
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'
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
(i)
18.29 m
(ii)
23.29 m
(iii)
20.29 m
(iv)
26.29 m
(v)
28.29 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 60°56'. If the height of the chimney is 1 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'
60
1.7321
1.7391
1.7461
1.7532
1.7603
1.7675
1.7747
1.7820
1.7893
1.7966
12
24
36
48
60
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
60
0.8660
0.8669
0.8678
0.8686
0.8695
0.8704
0.8712
0.8721
0.8729
0.8738
1
3
4
6
7
(i)
0.14 m
(ii)
3.14 m
(iii)
1.14 m
(iv)
2.14 m
(v)
9.14 m
Question
9
9.
From the top of a light house which is 80 m high from the sea level, the angles of depression of two ships are 60° 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)
97.37 m
(ii)
95.37 m
(iii)
92.37 m
(iv)
87.37 m
(v)
89.37 m
Question
10
10.
Two vertical poles are on either side of a road. A 24 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)
23.97 m
(ii)
28.97 m
(iii)
25.97 m
(iv)
33.97 m
(v)
31.97 m
Question
11
11.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60° 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.
(i)
709.10 m
(ii)
684.10 m
(iii)
723.10 m
(iv)
722.10 m
(v)
707.10 m
Question
12
12.
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 60°. If the height of the tower is 95 m, find the height of the building .
(i)
34.67 m
(ii)
28.67 m
(iii)
26.67 m
(iv)
36.67 m
(v)
31.67 m
Question
13
13.
A flagstaff stands on the top of a building at a distance of 20 m away from the foot of building . The angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 30°. Find the height of the flagstaff .
(i)
40
3
√
3
m
(ii)
40
m
(iii)
20
√
2
m
(iv)
40
3
m
(v)
40
3
√
18
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
sin
(-1)
(
1
4
)
.
If the distance between the point and the top of the
tower
is
170 m
,
find the height of the
tower
.
(i)
45.50 m
(ii)
39.50 m
(iii)
42.50 m
(iv)
47.50 m
(v)
37.50 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 49°59' and the angle of elevation of the top of the building is 29°31'. If the height of the flag staff is 11 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'
29
0.5543
0.5566
0.5589
0.5612
0.5635
0.5658
0.5681
0.5704
0.5727
0.5750
4
8
12
15
19
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
49
1.1504
1.1544
1.1585
1.1626
1.1667
1.1708
1.1750
1.1792
1.1833
1.1875
7
14
21
27
34
(i)
8.97 m
(ii)
7.97 m
(iii)
10.97 m
(iv)
9.97 m
(v)
11.97 m
Question
16
16.
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 32°12'. If the distance between the observation point and the foot of the radio tower is 4 m, find the height 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'
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
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)
2.52 m
(ii)
4.52 m
(iii)
1.52 m
(iv)
3.52 m
(v)
0.52 m
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 flag staff is 10 m, find the height of the building .
(i)
8.66 m
(ii)
13.66 m
(iii)
16.66 m
(iv)
18.66 m
(v)
10.66 m
Question
18
18.
A pole stands vertically on the ground. From a point on the ground, the angle of elevation of the top of the pole is found to be 31°56'. If the distance between the observation point and the top of the pole is 1 m, find the distance between the observation point and the foot of the pole.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
31
0.5150
0.5165
0.5780
0.5195
0.5210
0.5225
0.5240
0.5255
0.5270
0.5284
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'
31
0.8572
0.8563
0.8554
0.8545
0.8536
0.8526
0.8517
0.8508
0.8499
0.8490
2
3
5
6
8
(i)
2.85 m
(ii)
7.85 m
(iii)
0.85 m
(iv)
8.85 m
(v)
1.85 m
Question
19
19.
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 35°2'. If the distance between the observation point and the foot of the tower is 1 m, find the distance between the observation point and the top of the tower.
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)
1.22 m
(ii)
3.22 m
(iii)
0.22 m
(iv)
2.22 m
(v)
9.22 m
Question
20
20.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 170 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°33' and 42°43' respectively. Find the width of the river .
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'
42
0.9004
0.9036
0.9067
0.9099
0.9131
0.9163
0.9195
0.9228
0.9260
0.9293
5
11
16
21
27
(i)
184.12 m
(ii)
172.12 m
(iii)
209.12 m
(iv)
197.12 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 60° and the angle of depression of its foot is 45°. Find the height of the cable tower.
(i)
38.52 m
(ii)
35.52 m
(iii)
32.52 m
(iv)
40.52 m
(v)
30.52 m
Question
22
22.
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
110 m
,
find the distance between
the observation point and the top of the
chimney
.
(i)
220
m
(ii)
55
√
12
m
(iii)
110
√
2
m
(iv)
220
√
3
m
(v)
110
m
Question
23
23.
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 60° and 45° and the distance between them is 180 m , find the height of the cliff.
(i)
90.12 m
(ii)
131.12 m
(iii)
114.12 m
(iv)
139.12 m
(v)
102.12 m
Question
24
24.
The angle of elevation of the top of a building from the foot of a tower is 30°24'. The angle of elevation of the top of the tower from the foot of the building is 33°1'. If the height of the tower is 65 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'
30
0.5774
0.5797
0.5820
0.5844
0.5867
0.5890
0.5914
0.5938
0.5961
0.5985
4
8
12
16
20
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)
61.69 m
(ii)
58.69 m
(iii)
63.69 m
(iv)
55.69 m
(v)
53.69 m
Question
25
25.
An observer 1.8 m tall, is 10 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)
14.12 m
(ii)
16.12 m
(iii)
22.12 m
(iv)
24.12 m
(v)
19.12 m
Assignment Key
1) (ii)
2) (ii)
3) (iii)
4) (i)
5) (iv)
6) (i)
7) (ii)
8) (iii)
9) (iii)
10) (ii)
11) (i)
12) (v)
13) (i)
14) (iii)
15) (iv)
16) (i)
17) (ii)
18) (iii)
19) (i)
20) (i)
21) (ii)
22) (iii)
23) (iii)
24) (ii)
25) (v)
