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 light house which is 100 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)
78.19 m
(ii)
70.19 m
(iii)
68.19 m
(iv)
76.19 m
(v)
73.19 m
Question
2
2.
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)
∠c
(iii)
∠b
(iv)
∠d
Question
3
3.
Two poles of equal height are standing opposite to each other on either side of a road which is 45 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of each pole and the distances of the point from the two poles .
(i)
height =
19.49 m
, distances away =
33.75 m
,
11.25 m
(ii)
height =
18.49 m
, distances away =
32.75 m
,
10.25 m
(iii)
height =
17.49 m
, distances away =
31.75 m
,
9.25 m
(iv)
height =
20.49 m
, distances away =
34.75 m
,
12.25 m
(v)
height =
21.49 m
, distances away =
35.75 m
,
13.25 m
Question
4
4.
From the top of a 7 m high building , the angle of elevation of the top of a cable tower is 26°52' and the angle of depression of its foot is 23°52'. 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'
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'
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
(i)
12.01 m
(ii)
15.01 m
(iii)
20.01 m
(iv)
18.01 m
(v)
10.01 m
Question
5
5.
If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?
(i)
∠d
(ii)
∠e
(iii)
∠f
(iv)
∠c
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
cos
(-1)
(
2
3
)
.
If the distance between the point and the foot of the
tower
is
120 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
177.00 m
(ii)
166.00 m
(iii)
205.00 m
(iv)
193.00 m
(v)
180.00 m
Question
7
7.
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 opposite sides of the cliff .
(i)
339.85 m
(ii)
327.85 m
(iii)
315.85 m
(iv)
303.85 m
(v)
332.85 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 52°22'. If the distance between the observation point and the top of the tower is 18 m, find the distance between the observation point and the foot of the tower.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
52
0.7830
0.7891
0.7902
0.7912
0.7923
0.7934
0.7944
0.7955
0.7965
0.7976
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'
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)
10.99 m
(ii)
15.99 m
(iii)
7.99 m
(iv)
13.99 m
(v)
5.99 m
Question
9
9.
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
60°
.
If the distance between the point and the top of the
radio tower
is
200 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
99
m
(ii)
103
m
(iii)
101
m
(iv)
98
m
(v)
100
m
Question
10
10.
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
3
)
.
If the distance between the point and the top of the
tower
is
160 m
,
find the height of the
tower
.
(i)
48.33 m
(ii)
58.33 m
(iii)
50.33 m
(iv)
53.33 m
(v)
56.33 m
Question
11
11.
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 10 min for the angle of depression to change from 30° to 60°, how soon after this, will the car reach the observation tower?
(i)
4 min 4 sec
(ii)
5 min 0 sec
(iii)
6 min 6 sec
(iv)
2 min 3 sec
(v)
8 min 7 sec
Question
12
12.
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°40'. If the distance between the observation point and the top of the chimney is 10 m, find the height of the chimney.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
59
0.8572
0.8581
0.8590
0.8599
0.8607
0.8616
0.8625
0.8634
0.8643
0.8657
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'
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)
10.63 m
(ii)
6.63 m
(iii)
7.63 m
(iv)
9.63 m
(v)
8.63 m
Question
13
13.
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° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 7 m, find the height of the building .
(i)
8.56 m
(ii)
7.56 m
(iii)
11.56 m
(iv)
10.56 m
(v)
9.56 m
Question
14
14.
The angle of elevation of the top of a building from the foot of a tower is 32°43'. The angle of elevation of the top of the tower from the foot of the building is 50°9'. If the height of the tower is 35 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'
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 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)
18.76 m
(ii)
23.76 m
(iii)
13.76 m
(iv)
15.76 m
(v)
21.76 m
Question
15
15.
From a point 180 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 cliff.
(i)
103.93 m
(ii)
88.93 m
(iii)
97.93 m
(iv)
110.93 m
(v)
125.93 m
Question
16
16.
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 38°44'. If the height of the pole is 20 m, find the distance between the observation point and the top of the pole.
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
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
38
0.6157
0.6170
0.6184
0.6195
0.6211
0.6225
0.6239
0.6252
0.6266
0.6280
2
5
7
9
12
(i)
28.96 m
(ii)
31.96 m
(iii)
36.96 m
(iv)
26.96 m
(v)
34.96 m
Question
17
17.
A man in a boat rowing away from a lighthouse 75 m high, takes 1.5 min to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat.
(i)
8.96 m/sec
(ii)
1.96 m/sec
(iii)
0.96 m/sec
(iv)
7.96 m/sec
(v)
2.96 m/sec
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
tan
(-1)
(
4
9
)
.
If the height of the
tower
is
80 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
167.00 m
(ii)
196.00 m
(iii)
208.00 m
(iv)
180.00 m
(v)
172.00 m
Question
19
19.
Two vertical poles are on either side of a road. A 26 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 30° with the road. Find the width of the road.
(i)
32.52 m
(ii)
30.52 m
(iii)
38.52 m
(iv)
35.52 m
(v)
40.52 m
Question
20
20.
A man 1.7 m tall stands at a distance of 1.5 m from a lamp post and casts a shadow of 5.3 m on the ground. Find the height of the lamp post .
(i)
3.18 m
(ii)
1.18 m
(iii)
2.18 m
(iv)
4.18 m
(v)
0.18 m
Question
21
21.
An observer 1.8 m tall, is 190 m away from a tower . The angle of elevation of the top of the tower from her eyes is 30°. Find the height of the tower .
(i)
118.51 m
(ii)
135.51 m
(iii)
111.51 m
(iv)
109.51 m
(v)
86.51 m
Question
22
22.
From the top of a 11 m high building , the angle of elevation of the top of a cable tower is 45° and the angle of depression of its foot is 30°. Find the height of the cable tower.
(i)
35.05 m
(ii)
25.05 m
(iii)
30.05 m
(iv)
33.05 m
(v)
27.05 m
Question
23
23.
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°
.
If the distance between the point and the foot of the
building
is
70 m
,
find the distance between
the observation point and the top of the
building
.
(i)
142
m
(ii)
140
m
(iii)
141
m
(iv)
137
m
(v)
139
m
Question
24
24.
A
tower
stands vertically on the ground.
The height of the
tower
is
160
√
3
m
.
The distance between the observation point and its foot
is
480
m
.
Find the angle of elevation.
(i)
45°
(ii)
75°
(iii)
90°
(iv)
60°
(v)
30°
Question
25
25.
An observer 1.9 m tall, is 150 m away from a tower . The angle of elevation of the top of the tower from her eyes is 39°9'. 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'
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
(i)
110.03 m
(ii)
107.03 m
(iii)
126.03 m
(iv)
138.03 m
(v)
124.03 m
Assignment Key
1) (v)
2) (i)
3) (i)
4) (ii)
5) (ii)
6) (v)
7) (ii)
8) (i)
9) (v)
10) (iv)
11) (ii)
12) (v)
13) (v)
14) (i)
15) (i)
16) (ii)
17) (iii)
18) (iv)
19) (iv)
20) (iii)
21) (iii)
22) (iii)
23) (ii)
24) (v)
25) (v)
