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 130 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 37°37' and 27°19' 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'
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'
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)
64.14 m
(ii)
62.14 m
(iii)
70.14 m
(iv)
67.14 m
(v)
72.14 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 50°9' and 39°4' 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'
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
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)
30.05 m
(ii)
32.05 m
(iii)
24.05 m
(iv)
22.05 m
(v)
27.05 m
Question
3
3.
The angles of depression of two boats from the top of a cliff 130 m high are 22° and 48° 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'
68
2.4751
2.4876
2.5002
2.5129
2.5257
2.5386
2.5517
2.5679
2.5782
2.5916
22
43
65
87
108
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)
177.71 m
(ii)
212.71 m
(iii)
204.71 m
(iv)
202.71 m
(v)
220.71 m
Question
4
4.
The angles of depression of two boats from the top of a cliff 140 m high are 49° and 46° 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'
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'
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)
238.90 m
(ii)
256.90 m
(iii)
251.90 m
(iv)
270.90 m
(v)
269.90 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 13 min for the angle of depression to change from 22° to 27°, 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'
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'
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
(i)
51 min 49 sec
(ii)
48 min 46 sec
(iii)
50 min 48 sec
(iv)
49 min 47 sec
(v)
47 min 45 sec
Question
6
6.
From a point 150 m above a lake, the angle of elevation of a cloud is 31° and the angle of depression of its reflection in the lake is 62°. 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'
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'
62
1.8807
1.8887
1.8967
1.9047
1.9128
1.9210
1.9292
1.9375
1.9458
1.9542
14
27
41
55
68
(i)
297.86 m
(ii)
277.86 m
(iii)
276.86 m
(iv)
290.86 m
(v)
318.86 m
Question
7
7.
At the foot of a mountain, the elevation of its summit is 41°. After ascending 600 m towards the mountain up an incline of 25°, the elevation changes to 64°. 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'
64
2.0503
2.0594
2.0686
2.0778
2.0872
2.0965
2.1060
2.1155
2.1251
2.1348
16
31
47
63
78
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
25
0.9063
0.9056
0.9048
0.9041
0.9033
0.9026
0.9018
0.9011
0.9003
0.8996
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'
25
0.4226
0.4242
0.4258
0.4274
0.4289
0.4305
0.4321
0.4337
0.4352
0.4368
3
5
8
11
13
(i)
658.97 m
(ii)
633.97 m
(iii)
639.97 m
(iv)
607.97 m
(v)
626.97 m
Question
8
8.
The shadow of a vertical tower BA on a level ground is increased by 35 m, when the altitude of the sun changes from 56° to 36°. 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'
56
1.4826
1.4882
1.4938
1.4994
1.5051
1.5108
1.5166
1.5224
1.5282
1.5340
10
19
29
38
48
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)
44.86 m
(ii)
46.86 m
(iii)
54.86 m
(iv)
52.86 m
(v)
49.86 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 42° and 29° and the distance between them is 185 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'
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
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
(i)
58.47 m
(ii)
60.47 m
(iii)
63.47 m
(iv)
68.47 m
(v)
66.47 m
Question
10
10.
A man in a boat rowing away from a lighthouse 90 m high, takes 2.5 min to change the angle of elevation of the top of the lighthouse from 36° to 25°. 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'
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'
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)
1.46 m/sec
(ii)
0.46 m/sec
(iii)
8.46 m/sec
(iv)
7.46 m/sec
(v)
2.46 m/sec
Question
11
11.
Two vertical poles are on either side of a road. A 22 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 28°54' with the pole and when it is turned to rest against another pole, it makes an angle of 48°28' 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'
28
0.8829
0.8821
0.8813
0.8805
0.8796
0.8788
0.8780
0.8771
0.8763
0.8755
1
3
4
5
7
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
48
0.6691
0.6678
0.6665
0.6652
0.6639
0.6626
0.6613
0.6600
0.6587
0.6574
2
4
7
9
11
(i)
30.85 m
(ii)
36.85 m
(iii)
38.85 m
(iv)
28.85 m
(v)
33.85 m
Assignment Key
1) (iv)
2) (v)
3) (iii)
4) (ii)
5) (iv)
6) (iv)
7) (ii)
8) (v)
9) (iii)
10) (ii)
11) (v)
