EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Heights and Distances
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
From a point 110 m above a lake, the angle of elevation of a cloud is 32° and the angle of depression of its reflection in the lake is 58°. Find the height of the cloud from the lake.
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'
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
(i)
250.95 m
(ii)
274.95 m
(iii)
243.95 m
(iv)
222.95 m
(v)
262.95 m
Question
2
2.
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 55°48'. If the distance between the observation point and the top of the building is 3 m, find the height of the building.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
55
0.8192
0.8202
0.8211
0.8221
0.8231
0.8241
0.8251
0.8261
0.8271
0.8281
2
3
5
7
8
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
55
0.5736
0.5721
0.5707
0.5693
0.5678
0.5664
0.5650
0.5635
0.5621
0.5606
2
5
7
9
12
(i)
2.48 m
(ii)
1.48 m
(iii)
0.48 m
(iv)
3.48 m
(v)
4.48 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 45°. If the height of the building is 18 m, find the height of the flag staff .
(i)
8.18 m
(ii)
13.18 m
(iii)
10.18 m
(iv)
16.18 m
(v)
18.18 m
Question
4
4.
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
40 m
,
find the distance between
the observation point and the top of the
chimney
.
(i)
40
m
(ii)
80
√
3
m
(iii)
40
√
2
m
(iv)
80
m
(v)
20
√
12
m
Question
5
5.
Two vertical poles are on either side of a road. A 23 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)
31.42 m
(ii)
28.42 m
(iii)
36.42 m
(iv)
26.42 m
(v)
34.42 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
sec
(-1)
(
3
2
)
.
If the distance between the point and the top of the
tower
is
120 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
80.00 m
(ii)
85.00 m
(iii)
75.00 m
(iv)
83.00 m
(v)
77.00 m
Question
7
7.
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 110 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
279.56 m
(ii)
270.56 m
(iii)
265.56 m
(iv)
247.56 m
(v)
259.56 m
Question
8
8.
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
30°
.
If the distance between the point and the foot of the
building
is
50 m
,
find the height of the
building
.
(i)
25
√
2
m
(ii)
50
3
√
3
m
(iii)
50
3
√
18
m
(iv)
50
m
(v)
50
3
m
Question
9
9.
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
30°
.
If the distance between the point and the top of the
building
is
170 m
,
find the distance between
the observation point and the foot of the
building
.
(i)
85
√
18
m
(ii)
255
2
√
2
m
(iii)
85
√
3
m
(iv)
255
m
(v)
85
m
Question
10
10.
A man in a boat rowing away from a lighthouse 35 m high, takes 4.5 min to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat.
(i)
8.15 m/sec
(ii)
0.15 m/sec
(iii)
2.15 m/sec
(iv)
1.15 m/sec
(v)
7.15 m/sec
Question
11
11.
From the top of a 20 m high building , the angle of elevation of the top of a cable tower is 32°30' and the angle of depression of its foot is 20°49'. 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'
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'
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)
48.51 m
(ii)
56.51 m
(iii)
58.51 m
(iv)
50.51 m
(v)
53.51 m
Question
12
12.
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 47° to 49°, how soon after this, will the car reach the observation 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 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)
275 min 59 sec
(ii)
277 min 60 sec
(iii)
272 min 56 sec
(iv)
274 min 58 sec
(v)
273 min 57 sec
Question
13
13.
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
30°
.
If the height of the
radio tower
is
130 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
195
√
2
m
(ii)
390
m
(iii)
130
√
3
m
(iv)
130
m
(v)
130
√
18
m
Question
14
14.
From a point 160 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)
95.38 m
(ii)
92.38 m
(iii)
97.38 m
(iv)
87.38 m
(v)
89.38 m
Question
15
15.
The angles of depression of two boats from the top of a cliff 160 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)
397.52 m
(ii)
369.52 m
(iii)
364.52 m
(iv)
353.52 m
(v)
376.52 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 38°57' and the angle of elevation of the top of the building is 26°57'. If the height of the building is 6 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'
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
(i)
3.54 m
(ii)
5.54 m
(iii)
1.54 m
(iv)
4.54 m
(v)
2.54 m
Question
17
17.
The shadow of a vertical tower BA on a level ground is increased by 40 m, when the altitude of the sun changes from 50° to 37°. 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'
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'
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)
81.98 m
(ii)
84.98 m
(iii)
86.98 m
(iv)
78.98 m
(v)
76.98 m
Question
18
18.
A man 1.6 m tall stands at a distance of 1.9 m from a lamp post and casts a shadow of 4.4 m on the ground. Find the height of the lamp post .
(i)
4.29 m
(ii)
0.29 m
(iii)
2.29 m
(iv)
1.29 m
(v)
3.29 m
Question
19
19.
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 flag staff is 14 m, find the height of the building .
(i)
5.00 m
(ii)
6.00 m
(iii)
8.00 m
(iv)
7.00 m
(v)
9.00 m
Question
20
20.
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
5
)
.
If the distance between the point and the foot of the
tower
is
90 m
,
find the height of the
tower
.
(i)
13.00 m
(ii)
15.00 m
(iii)
18.00 m
(iv)
21.00 m
(v)
23.00 m
Question
21
21.
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 32°8'. If the height of the pole is 6 m, find the distance between the observation point and the foot of the pole.
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)
10.55 m
(ii)
7.55 m
(iii)
8.55 m
(iv)
9.55 m
(v)
11.55 m
Question
22
22.
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 44° and 37° and the distance between them is 215 m , find the height of the cliff.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
44
0.9657
0.9691
0.9725
0.9759
0.9793
0.9827
0.9861
0.9896
0.9930
0.9965
6
11
17
23
28
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)
86.01 m
(ii)
88.01 m
(iii)
94.01 m
(iv)
96.01 m
(v)
91.01 m
Question
23
23.
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 49°31' and 24°58' 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'
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
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
24
0.4452
0.4473
0.4494
0.4515
0.4536
0.4557
0.4578
0.4599
0.4621
0.4642
4
7
11
14
18
(i)
height =
13.66 m
, distances away =
27.05 m
,
11.95 m
(ii)
height =
10.66 m
, distances away =
24.05 m
,
8.95 m
(iii)
height =
11.66 m
, distances away =
25.05 m
,
9.95 m
(iv)
height =
9.66 m
, distances away =
23.05 m
,
7.95 m
(v)
height =
12.66 m
, distances away =
26.05 m
,
10.95 m
Question
24
24.
The angles of depression of two boats from the top of a cliff 120 m high are 60° and 30° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
(i)
126.56 m
(ii)
124.56 m
(iii)
161.56 m
(iv)
138.56 m
(v)
141.56 m
Question
25
25.
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
130 m
,
find the height of the
tower
.
(i)
198.33 m
(ii)
173.33 m
(iii)
151.33 m
(iv)
187.33 m
(v)
157.33 m
Assignment Key
1) (i)
2) (i)
3) (ii)
4) (iii)
5) (i)
6) (i)
7) (iii)
8) (ii)
9) (iii)
10) (ii)
11) (v)
12) (iv)
13) (iii)
14) (ii)
15) (ii)
16) (i)
17) (i)
18) (iii)
19) (iv)
20) (iii)
21) (iv)
22) (v)
23) (iii)
24) (iv)
25) (ii)
