EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Heights and Distances
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
A man in a boat rowing away from a lighthouse 50 m high, takes 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)
8.12 m/sec
(ii)
2.12 m/sec
(iii)
1.12 m/sec
(iv)
0.12 m/sec
(v)
7.12 m/sec
Question
2
2.
From the top of a light house which is 55 m high from the sea level, the angles of depression of two ships are 48°37' and 42°34'. 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'
48
1.1106
1.1145
1.1184
1.1224
1.1263
1.1303
1.1343
1.1383
1.1423
1.1463
7
13
20
27
33
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)
16.43 m
(ii)
11.43 m
(iii)
6.43 m
(iv)
8.43 m
(v)
14.43 m
Question
3
3.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 43°58' 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.
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
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)
42.08 m
(ii)
52.08 m
(iii)
50.08 m
(iv)
44.08 m
(v)
47.08 m
Question
4
4.
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 30° and the distance between them is 145 m , find the height of the cliff.
(i)
65.79 m
(ii)
62.79 m
(iii)
57.79 m
(iv)
67.79 m
(v)
59.79 m
Question
5
5.
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 58°32'. If the height of the chimney is 20 m, find the distance between the observation point and the foot of the chimney.
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
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
58
0.8450
0.8490
0.8499
0.8508
0.8517
0.8526
0.8536
0.8545
0.8554
0.8563
2
3
5
6
8
(i)
12.24 m
(ii)
15.24 m
(iii)
17.24 m
(iv)
7.24 m
(v)
9.24 m
Question
6
6.
An aeroplane is flying horizontally 1100 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 54°. After 30 sec , its elevation from the same point changes to 34°. 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'
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'
54
1.3764
1.3814
1.3865
1.3916
1.3968
1.4019
1.4071
1.4124
1.4176
1.4229
9
17
26
34
43
(i)
94.80 kmph
(ii)
96.80 kmph
(iii)
104.80 kmph
(iv)
99.80 kmph
(v)
102.80 kmph
Question
7
7.
At the foot of a mountain, the elevation of its summit is 41°. After ascending 900 m towards the mountain up an incline of 30°, the elevation changes to 66°. Find the height of the mountain.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
41
0.8693
0.8724
0.8754
0.8785
0.8816
0.8847
0.8878
0.8910
0.8941
0.8972
5
10
16
21
26
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
66
2.2460
2.2566
2.2673
2.2781
2.2889
2.2998
2.3109
2.3220
2.3332
2.3445
18
37
55
73
92
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
30
0.8660
0.8652
0.8643
0.8634
0.8625
0.8616
0.8607
0.8599
0.8590
0.8581
1
3
4
6
7
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
30
0.5000
0.5015
0.5030
0.5045
0.5060
0.5075
0.5090
0.5105
0.5120
0.5135
3
5
8
10
13
(i)
815.15 m
(ii)
794.15 m
(iii)
829.15 m
(iv)
821.15 m
(v)
833.15 m
Question
8
8.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 90 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 33°12' and 44°38' 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'
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
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
(i)
94.17 m
(ii)
91.17 m
(iii)
88.17 m
(iv)
86.17 m
(v)
96.17 m
Question
9
9.
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 30° and 60° respectively. Find the height of each pole and the distances of the point from the two poles .
(i)
height =
10.99 m
, distances away =
5.5 m
,
20.5 m
(ii)
height =
11.99 m
, distances away =
6.5 m
,
21.5 m
(iii)
height =
12.99 m
, distances away =
7.5 m
,
22.5 m
(iv)
height =
14.99 m
, distances away =
9.5 m
,
24.5 m
(v)
height =
13.99 m
, distances away =
8.5 m
,
23.5 m
Question
10
10.
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 height of the
radio tower
is
50 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
50
3
√
18
m
(ii)
25
√
2
m
(iii)
50
m
(iv)
50
3
√
3
m
(v)
50
3
m
Question
11
11.
A man 1.3 m tall stands at a distance of 8.3 m from a lamp post and casts a shadow of 1.3 m on the ground. Find the height of the lamp post .
(i)
9.60 m
(ii)
11.60 m
(iii)
10.60 m
(iv)
8.60 m
(v)
7.60 m
Question
12
12.
From a point 180 m above a lake, the angle of elevation of a cloud is 27° and the angle of depression of its reflection in the lake is 57°. 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'
27
0.5095
0.5117
0.5139
0.5161
0.5184
0.5206
0.5228
0.5250
0.5272
0.5295
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'
57
1.5399
1.5458
1.5517
1.5577
1.5637
1.5697
1.5757
1.5818
1.5880
1.5941
10
20
30
40
50
(i)
332.01 m
(ii)
385.01 m
(iii)
340.01 m
(iv)
363.01 m
(v)
358.01 m
Question
13
13.
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 45°. If the height of the tower is 70 m, find the height of the building .
(i)
37.42 m
(ii)
43.42 m
(iii)
40.42 m
(iv)
35.42 m
(v)
45.42 m
Question
14
14.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 200 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 width of the river .
(i)
140.47 m
(ii)
132.47 m
(iii)
92.47 m
(iv)
111.47 m
(v)
115.47 m
Question
15
15.
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 40 m from the foot of the tree . Find the height of the tree before it was broken.
(i)
66.29 m
(ii)
64.29 m
(iii)
74.29 m
(iv)
69.29 m
(v)
72.29 m
Question
16
16.
An observer 1.9 m tall, is 50 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)
85.51 m
(ii)
91.51 m
(iii)
93.51 m
(iv)
83.51 m
(v)
88.51 m
Question
17
17.
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 distance between the point and the top of the
radio tower
is
90 m
,
find the distance between
the observation point and the foot of the
radio tower
.
(i)
45
m
(ii)
135
m
(iii)
45
√
18
m
(iv)
135
2
√
2
m
(v)
45
√
3
m
Question
18
18.
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 foot of the
building
is
190 m
,
find the distance between
the observation point and the top of the
building
.
(i)
190
√
2
m
(ii)
380
m
(iii)
95
√
12
m
(iv)
380
√
3
m
(v)
190
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
tan
(-1)
(
1
2
)
.
If the height of the
tower
is
80 m
,
find the distance between
the observation point and the foot of the
tower
.
(i)
160.00 m
(ii)
163.00 m
(iii)
138.00 m
(iv)
146.00 m
(v)
174.00 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
cos
(-1)
(
5
9
)
.
If the distance between the point and the foot of the
tower
is
10 m
,
find the distance between
the observation point and the top of the
tower
.
(i)
18.00 m
(ii)
15.00 m
(iii)
13.00 m
(iv)
21.00 m
(v)
23.00 m
Question
21
21.
From a point 70 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 60° and 30° respectively. Find the height of the cliff.
(i)
35.42 m
(ii)
43.42 m
(iii)
37.42 m
(iv)
45.42 m
(v)
40.42 m
Question
22
22.
An observer 1.7 m tall, is 100 m away from a tower . The angle of elevation of the top of the tower from her eyes is 32°20'. 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'
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
(i)
70.00 m
(ii)
65.00 m
(iii)
62.00 m
(iv)
68.00 m
(v)
60.00 m
Question
23
23.
A man in a boat rowing away from a lighthouse 65 m high, takes 2 min to change the angle of elevation of the top of the lighthouse from 36° to 29°. Find the speed of the boat.
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'
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)
7.23 m/sec
(ii)
2.23 m/sec
(iii)
1.23 m/sec
(iv)
0.23 m/sec
(v)
8.23 m/sec
Question
24
24.
A flagstaff stands on the top of a building at a distance of 40 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
√
2
m
(ii)
80
3
√
18
m
(iii)
80
3
m
(iv)
80
3
√
3
m
(v)
80
m
Question
25
25.
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 55°4'. If the distance between the observation point and the top of the radio tower is 13 m, find the distance between the observation point and the foot of the radio tower.
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)
6.45 m
(ii)
8.45 m
(iii)
7.45 m
(iv)
5.45 m
(v)
9.45 m
Assignment Key
1) (iv)
2) (ii)
3) (v)
4) (ii)
5) (i)
6) (iv)
7) (iv)
8) (ii)
9) (iii)
10) (iv)
11) (i)
12) (v)
13) (iii)
14) (v)
15) (iv)
16) (v)
17) (v)
18) (i)
19) (i)
20) (i)
21) (v)
22) (ii)
23) (iv)
24) (iv)
25) (iii)
