EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Some Applications of Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
Two poles of equal height are standing opposite to each other on either side of a road which is 35 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 40°40' and 42°9' 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'
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
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)
height =
14.43 m
, distances away =
16.04 m
,
16.96 m
(ii)
height =
13.43 m
, distances away =
15.04 m
,
15.96 m
(iii)
height =
17.43 m
, distances away =
19.04 m
,
19.96 m
(iv)
height =
15.43 m
, distances away =
17.04 m
,
17.96 m
(v)
height =
16.43 m
, distances away =
18.04 m
,
18.96 m
Question
2
2.
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 43°49'. If the distance between the observation point and the top of the tower is 8 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'
43
0.6820
0.6833
0.6845
0.6858
0.6871
0.6884
0.6896
0.6909
0.6921
0.6934
2
4
6
9
11
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
43
0.7314
0.7302
0.7290
0.7278
0.7266
0.7254
0.7242
0.7230
0.7218
0.7206
2
4
6
8
10
(i)
3.77 m
(ii)
7.77 m
(iii)
6.77 m
(iv)
4.77 m
(v)
5.77 m
Question
3
3.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 30 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 50°28' and 63°19' 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'
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 Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
63
1.9626
1.9711
1.9797
1.9883
1.9970
2.0057
2.0145
2.0233
2.0323
2.0413
15
29
44
58
73
(i)
16.73 m
(ii)
11.73 m
(iii)
8.73 m
(iv)
6.73 m
(v)
14.73 m
Question
4
4.
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 same side of the cliff .
(i)
90.85 m
(ii)
82.85 m
(iii)
92.85 m
(iv)
87.85 m
(v)
84.85 m
Question
5
5.
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 building is 9 m, find the height of the flag staff .
(i)
8.59 m
(ii)
6.59 m
(iii)
5.59 m
(iv)
7.59 m
(v)
4.59 m
Question
6
6.
The angles of depression of two boats from the top of a cliff 170 m high are 60° and 30° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
(i)
408.62 m
(ii)
384.62 m
(iii)
415.62 m
(iv)
367.62 m
(v)
392.62 m
Question
7
7.
An observer 1.7 m tall, is 180 m away from a tower . The angle of elevation of the top of the tower from her eyes is 33°24'. 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)
96.39 m
(ii)
147.39 m
(iii)
105.39 m
(iv)
120.39 m
(v)
138.39 m
Question
8
8.
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 20 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
45.28 m
(ii)
43.28 m
(iii)
53.28 m
(iv)
48.28 m
(v)
51.28 m
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)
(
3
4
)
.
If the distance between the point and the foot of the
tower
is
70 m
,
find the height of the
tower
.
(i)
93.33 m
(ii)
88.33 m
(iii)
90.33 m
(iv)
96.33 m
(v)
98.33 m
Question
10
10.
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
30°
.
If the height of the
chimney
is
60 m
,
find the distance between
the observation point and the top of the
chimney
.
(i)
119
m
(ii)
122
m
(iii)
121
m
(iv)
118
m
(v)
120
m
Question
11
11.
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°
.
If the distance between the point and the top of the
chimney
is
130 m
,
find the distance between
the observation point and the foot of the
chimney
.
(i)
65
m
(ii)
63
m
(iii)
66
m
(iv)
68
m
(v)
64
m
Question
12
12.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 47°37' 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.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
47
1.0724
1.0761
1.0799
1.0837
1.0875
1.0913
1.0951
1.0990
1.1028
1.1067
6
13
19
25
32
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)
98.17 m
(ii)
121.17 m
(iii)
76.17 m
(iv)
103.17 m
(v)
117.17 m
Question
13
13.
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)
(
7
9
)
.
If the distance between the point and the top of the
tower
is
180 m
,
find the height of the
tower
.
(i)
132.00 m
(ii)
144.00 m
(iii)
153.00 m
(iv)
125.00 m
(v)
140.00 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 60°40'. If the distance between the observation point and the top of the tower is 13 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'
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)
11.33 m
(ii)
14.33 m
(iii)
16.33 m
(iv)
8.33 m
(v)
6.33 m
Question
15
15.
The angle of elevation of the top of a building from the foot of a tower is 40°42'. The angle of elevation of the top of the tower from the foot of the building is 36°35'. 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'
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
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)
40.55 m
(ii)
35.55 m
(iii)
37.55 m
(iv)
43.55 m
(v)
45.55 m
Question
16
16.
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 26°26' and the angle of elevation of the top of the building is 25°17'. If the height of the building is 16 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'
25
0.4663
0.4684
0.4706
0.4727
0.4748
0.4770
0.4791
0.4813
0.4834
0.4856
4
7
11
14
18
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
(i)
0.84 m
(ii)
1.84 m
(iii)
8.84 m
(iv)
2.84 m
(v)
7.84 m
Question
17
17.
Two poles of equal height are standing opposite to each other on either side of a road which is 20 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 =
7.32 m
, distances away =
12.68 m
,
7.32 m
(ii)
height =
9.32 m
, distances away =
14.68 m
,
9.32 m
(iii)
height =
5.32 m
, distances away =
10.68 m
,
5.32 m
(iv)
height =
8.32 m
, distances away =
13.68 m
,
8.32 m
(v)
height =
6.32 m
, distances away =
11.68 m
,
6.32 m
Question
18
18.
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)
∠d
(iii)
∠c
(iv)
∠e
Question
19
19.
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 45 m, find the height of the building .
(i)
25.98 m
(ii)
30.98 m
(iii)
20.98 m
(iv)
22.98 m
(v)
28.98 m
Question
20
20.
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°
.
If the distance between the point and the foot of the
chimney
is
190 m
,
find the height of the
chimney
.
(i)
190
√
3
m
(ii)
570
m
(iii)
285
√
2
m
(iv)
190
√
18
m
(v)
190
m
Question
21
21.
Two vertical poles are on either side of a road. A 27 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)
36.88 m
(ii)
33.88 m
(iii)
31.88 m
(iv)
41.88 m
(v)
39.88 m
Question
22
22.
A person, walking 10 m from a point toward a flagpost , observes that its angle of elevation changes from 45° to 60°. Find the height of the flagpost .
(i)
150
m
(ii)
(
15
+
5
√
3
)
m
(iii)
(
15
2
√
6
+
15
2
√
2
)
m
(iv)
(
2
+
√
3
)
m
(v)
(
15
√
6
+
5
√
18
)
m
Question
23
23.
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 12 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?
(i)
18 min 26 sec
(ii)
17 min 25 sec
(iii)
15 min 23 sec
(iv)
16 min 24 sec
(v)
13 min 21 sec
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 47°33'. If the distance between the observation point and the foot of the tower is 17 m, 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'
47
1.0724
1.0761
1.0799
1.0837
1.0875
1.0913
1.0951
1.0990
1.1028
1.1067
6
13
19
25
32
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)
23.58 m
(ii)
13.58 m
(iii)
21.58 m
(iv)
15.58 m
(v)
18.58 m
Question
25
25.
From the top of a 11 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)
35.05 m
(ii)
33.05 m
(iii)
25.05 m
(iv)
27.05 m
(v)
30.05 m
Assignment Key
1) (iv)
2) (v)
3) (ii)
4) (iv)
5) (ii)
6) (v)
7) (iv)
8) (iv)
9) (i)
10) (v)
11) (i)
12) (iv)
13) (v)
14) (i)
15) (i)
16) (i)
17) (i)
18) (iii)
19) (i)
20) (i)
21) (i)
22) (ii)
23) (iv)
24) (v)
25) (v)
