EduSahara™ Assignment
Name : Heights and Distances using Tables - 2
Chapter : Heights and Distances
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
From a point 50 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 39°3' and 28°15' respectively. 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'
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'
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)
21.86 m
(ii)
23.86 m
(iii)
31.86 m
(iv)
29.86 m
(v)
26.86 m
Question
2
2.
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 34°39' and 22°38' respectively. Find the height of the pillar.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
22
0.4040
0.4061
0.4081
0.4101
0.4122
0.4142
0.4163
0.4183
0.4202
0.4224
3
7
10
13
17
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
(i)
16.19 m
(ii)
22.19 m
(iii)
24.19 m
(iv)
14.19 m
(v)
19.19 m
Question
3
3.
The angles of depression of two boats from the top of a cliff 190 m high are 36° and 43° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
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
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
(i)
54.76 m
(ii)
52.76 m
(iii)
62.76 m
(iv)
60.76 m
(v)
57.76 m
Question
4
4.
The angles of depression of two boats from the top of a cliff 130 m high are 21° and 24° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
69
2.6051
2.6187
2.6325
2.6464
2.6605
2.6746
2.6889
2.7034
2.7179
2.7326
24
47
71
95
119
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
(i)
617.64 m
(ii)
644.64 m
(iii)
623.64 m
(iv)
636.64 m
(v)
630.64 m
Question
5
5.
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 31° to 36°, 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'
31
0.6009
0.6032
0.6056
0.6080
0.6104
0.6128
0.6152
0.6176
0.6200
0.6224
4
8
12
16
20
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)
45 min 47 sec
(ii)
46 min 49 sec
(iii)
50 min 52 sec
(iv)
47 min 50 sec
(v)
48 min 51 sec
Question
6
6.
From a point 200 m above a lake, the angle of elevation of a cloud is 34° 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'
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'
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)
528.76 m
(ii)
511.76 m
(iii)
499.76 m
(iv)
527.76 m
(v)
494.76 m
Question
7
7.
At the foot of a mountain, the elevation of its summit is 48°. After ascending 500 m towards the mountain up an incline of 27°, the elevation changes to 70°. 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'
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'
70
2.7475
2.7625
2.7776
2.7929
2.8083
2.8239
2.8397
2.8556
2.8716
2.8878
26
52
78
104
133
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
27
0.8910
0.8902
0.8894
0.8886
0.8878
0.8870
0.8862
0.8854
0.8846
0.8838
1
3
4
5
7
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
27
0.4540
0.4555
0.4571
0.4586
0.4602
0.4617
0.4633
0.4648
0.4664
0.4679
3
5
8
11
13
(i)
662.47 m
(ii)
676.47 m
(iii)
691.47 m
(iv)
648.47 m
(v)
679.47 m
Question
8
8.
The shadow of a vertical tower BA on a level ground is increased by 50 m, when the altitude of the sun changes from 48° to 31°. 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'
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'
31
0.6009
0.6032
0.6056
0.6080
0.6104
0.6128
0.6152
0.6176
0.6200
0.6224
4
8
12
16
20
(i)
60.47 m
(ii)
70.47 m
(iii)
68.47 m
(iv)
62.47 m
(v)
65.47 m
Question
9
9.
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 37° and 41° and the distance between them is 140 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'
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
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
(i)
61.51 m
(ii)
51.51 m
(iii)
53.51 m
(iv)
59.51 m
(v)
56.51 m
Question
10
10.
A man in a boat rowing away from a lighthouse 65 m high, takes 2.5 min to change the angle of elevation of the top of the lighthouse from 50° to 20°. 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'
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
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)
8.83 m/sec
(ii)
7.83 m/sec
(iii)
2.83 m/sec
(iv)
1.83 m/sec
(v)
0.83 m/sec
Question
11
11.
Two vertical poles are on either side of a road. A 30 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 29°15' with the pole and when it is turned to rest against another pole, it makes an angle of 45°11' with the road. Find the width of the road.
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
29
0.8746
0.8738
0.8729
0.8721
0.8712
0.8704
0.8695
0.8686
0.8678
0.8669
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'
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)
44.32 m
(ii)
52.32 m
(iii)
47.32 m
(iv)
50.32 m
(v)
42.32 m
Assignment Key
1) (v)
2) (v)
3) (v)
4) (v)
5) (iv)
6) (ii)
7) (ii)
8) (v)
9) (v)
10) (v)
11) (iii)
