EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Some Applications of Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
A man in a boat rowing away from a lighthouse 90 m high, takes 3.5 min to change the angle of elevation of the top of the lighthouse from 45° to 30°. Find the speed of the boat.
(i)
2.31 m/sec
(ii)
0.31 m/sec
(iii)
8.31 m/sec
(iv)
1.31 m/sec
(v)
7.31 m/sec
Question
2
2.
From the top of a 20 m high building , the angle of elevation of the top of a cable tower is 34°17' and the angle of depression of its foot is 20°45'. 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'
34
0.6745
0.6771
0.6796
0.6822
0.6847
0.6873
0.6899
0.6924
0.6930
0.6976
4
9
13
17
22
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
(i)
52.99 m
(ii)
55.99 m
(iii)
50.99 m
(iv)
58.99 m
(v)
60.99 m
Question
3
3.
Two poles of equal height are standing opposite to each other on either side of a road which is 30 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 23°17' and 36°16' 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'
23
0.4245
0.4265
0.4286
0.4307
0.4327
0.4348
0.4369
0.4390
0.4411
0.4431
3
7
10
14
17
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
36
0.7265
0.7292
0.7319
0.7346
0.7373
0.7400
0.7427
0.7454
0.7481
0.7508
5
9
14
18
23
(i)
height =
6.14 m
, distances away =
9.09 m
,
16.91 m
(ii)
height =
9.14 m
, distances away =
12.09 m
,
19.91 m
(iii)
height =
8.14 m
, distances away =
11.09 m
,
18.91 m
(iv)
height =
10.14 m
, distances away =
13.09 m
,
20.91 m
(v)
height =
7.14 m
, distances away =
10.09 m
,
17.91 m
Question
4
4.
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)
7 min 32 sec
(ii)
10 min 35 sec
(iii)
11 min 37 sec
(iv)
8 min 33 sec
(v)
9 min 34 sec
Question
5
5.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 150 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 34°37' and 40°34' 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'
34
0.6745
0.6771
0.6796
0.6822
0.6847
0.6873
0.6899
0.6924
0.6930
0.6976
4
9
13
17
22
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)
26.05 m
(ii)
34.05 m
(iii)
29.05 m
(iv)
24.05 m
(v)
32.05 m
Question
6
6.
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
√
18
m
(v)
40
3
m
Question
7
7.
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 60°27'. If the distance between the observation point and the top of the building is 10 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'
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
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
60
0.5000
0.4985
0.4970
0.4955
0.4939
0.4924
0.4909
0.4894
0.4879
0.4863
3
5
8
10
13
(i)
5.93 m
(ii)
4.93 m
(iii)
2.93 m
(iv)
6.93 m
(v)
3.93 m
Question
8
8.
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)
∠f
(ii)
∠g
(iii)
∠d
(iv)
∠e
Question
9
9.
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)
(
1
4
)
.
If the distance between the point and the foot of the
tower
is
50 m
,
find the height of the
tower
.
(i)
214.00 m
(ii)
187.00 m
(iii)
213.00 m
(iv)
200.00 m
(v)
172.00 m
Question
10
10.
A
tower
stands vertically on the ground.
The height of the
tower
is
20
m
.
The distance between the observation point and its top
is
40
m
.
Find the angle of elevation.
(i)
45°
(ii)
60°
(iii)
30°
(iv)
75°
(v)
90°
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
sin
(-1)
(
1
4
)
.
If the distance between the point and the top of the
tower
is
130 m
,
find the height of the
tower
.
(i)
27.50 m
(ii)
35.50 m
(iii)
32.50 m
(iv)
29.50 m
(v)
37.50 m
Question
12
12.
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 53°30'. If the distance between the observation point and the foot of the building is 1 m, find the distance between the observation point and the top of the building.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
53
1.3270
1.3319
1.3367
1.3416
1.3465
1.3514
1.3564
1.3613
1.3663
1.3713
8
16
25
33
41
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
53
0.6018
0.6004
0.5990
0.5976
0.5962
0.5948
0.5934
0.5920
0.5906
0.5892
2
5
7
9
12
(i)
0.68 m
(ii)
9.68 m
(iii)
1.68 m
(iv)
3.68 m
(v)
2.68 m
Question
13
13.
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 top of the
building
is
80 m
,
find the distance between
the observation point and the foot of the
building
.
(i)
20
√
12
m
(ii)
40
√
2
m
(iii)
40
m
(iv)
80
√
3
m
(v)
80
m
Question
14
14.
A man 1.6 m tall stands at a distance of 3.8 m from a lamp post and casts a shadow of 3.3 m on the ground. Find the height of the lamp post .
(i)
4.44 m
(ii)
2.44 m
(iii)
3.44 m
(iv)
5.44 m
(v)
1.44 m
Question
15
15.
The angles of depression of two boats from the top of a cliff 140 m high are 30° and 60° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
(i)
323.33 m
(ii)
307.33 m
(iii)
340.33 m
(iv)
338.33 m
(v)
305.33 m
Question
16
16.
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
7
)
.
If the height of the
tower
is
180 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
1260.00 m
(ii)
1040.00 m
(iii)
1200.00 m
(iv)
1530.00 m
(v)
1280.00 m
Question
17
17.
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)
(
4
7
)
.
If the distance between the point and the foot of the
tower
is
140 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
245.00 m
(ii)
271.00 m
(iii)
232.00 m
(iv)
260.00 m
Question
18
18.
From the top of a light house which is 45 m high from the sea level, the angles of depression of two ships are 60° and 45°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
(i)
19.02 m
(ii)
24.02 m
(iii)
14.02 m
(iv)
22.02 m
(v)
16.02 m
Question
19
19.
From the top of a light house which is 30 m high from the sea level, the angles of depression of two ships are 46°14' and 29°14'. 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'
46
1.0355
1.0392
1.0428
1.0464
1.0501
1.0538
1.0575
1.0612
1.0649
1.0686
6
12
18
25
31
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
(i)
24.86 m
(ii)
27.86 m
(iii)
29.86 m
(iv)
19.86 m
(v)
21.86 m
Question
20
20.
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 45°19'. If the distance between the observation point and the top of the pole is 12 m, find the height of the pole.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
45
0.7071
0.7083
0.7096
0.7108
0.7120
0.7133
0.7145
0.7157
0.7169
0.7181
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'
45
0.7071
0.7059
0.7046
0.7034
0.7022
0.7009
0.6997
0.6984
0.6972
0.6959
2
4
6
8
10
(i)
6.53 m
(ii)
7.53 m
(iii)
10.53 m
(iv)
9.53 m
(v)
8.53 m
Question
21
21.
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 6 m, find the height of the building .
(i)
6.20 m
(ii)
8.20 m
(iii)
7.20 m
(iv)
9.20 m
(v)
10.20 m
Question
22
22.
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 45° and 60° respectively. Find the width of the river .
(i)
4.77 m
(ii)
7.77 m
(iii)
5.77 m
(iv)
3.77 m
(v)
6.77 m
Question
23
23.
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 50 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
91.61 m
(ii)
81.61 m
(iii)
86.61 m
(iv)
89.61 m
(v)
83.61 m
Question
24
24.
An observer 1.7 m tall, is 160 m away from a tower . The angle of elevation of the top of the tower from her eyes is 33°56'. 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)
114.35 m
(ii)
109.35 m
(iii)
101.35 m
(iv)
135.35 m
(v)
97.35 m
Question
25
25.
An aeroplane is flying horizontally 900 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 43°. After 10 sec , its elevation from the same point changes to 28°. 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'
28
0.5317
0.5340
0.5362
0.5384
0.5407
0.5430
0.5452
0.5475
0.5498
0.5520
4
8
11
15
19
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
43
0.9325
0.9358
0.9391
0.9424
0.9457
0.9490
0.9523
0.9556
0.9590
0.9623
6
11
17
22
28
(i)
284.91 kmph
(ii)
247.91 kmph
(iii)
261.91 kmph
(iv)
239.91 kmph
(v)
276.91 kmph
Assignment Key
1) (ii)
2) (ii)
3) (iii)
4) (v)
5) (iii)
6) (i)
7) (ii)
8) (iii)
9) (iv)
10) (iii)
11) (iii)
12) (iii)
13) (ii)
14) (iii)
15) (i)
16) (i)
17) (i)
18) (i)
19) (i)
20) (v)
21) (ii)
22) (iii)
23) (iii)
24) (ii)
25) (iii)
