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 90 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°48' and 31°46' 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'
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'
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)
50.73 m
(ii)
58.73 m
(iii)
52.73 m
(iv)
60.73 m
(v)
55.73 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 43°42' and 40°11' 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'
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'
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
(i)
5.77 m
(ii)
6.77 m
(iii)
9.77 m
(iv)
8.77 m
(v)
7.77 m
Question
3
3.
The angles of depression of two boats from the top of a cliff 70 m high are 21° and 33° 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'
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'
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)
69.56 m
(ii)
71.56 m
(iii)
74.56 m
(iv)
79.56 m
(v)
77.56 m
Question
4
4.
The angles of depression of two boats from the top of a cliff 70 m high are 49° and 25° 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'
65
2.1445
2.1543
2.1642
2.1742
2.1842
2.1943
2.2045
2.2148
2.2251
2.2355
17
34
51
68
85
(i)
215.97 m
(ii)
203.97 m
(iii)
194.97 m
(iv)
232.97 m
(v)
210.97 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 5 min for the angle of depression to change from 23° to 41°, 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'
23
0.4245
0.4265
0.4286
0.4307
0.4327
0.4348
0.4369
0.4390
0.4411
0.4431
3
7
10
14
17
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)
4 min 46 sec
(ii)
2 min 43 sec
(iii)
6 min 48 sec
(iv)
5 min 47 sec
(v)
3 min 45 sec
Question
6
6.
From a point 70 m above a lake, the angle of elevation of a cloud is 25° and the angle of depression of its reflection in the lake is 60°. 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'
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'
60
1.7321
1.7391
1.7461
1.7532
1.7603
1.7675
1.7747
1.7820
1.7893
1.7966
12
24
36
48
60
(i)
105.57 m
(ii)
129.57 m
(iii)
138.57 m
(iv)
121.57 m
Question
7
7.
At the foot of a mountain, the elevation of its summit is 44°. After ascending 600 m towards the mountain up an incline of 25°, the elevation changes to 62°. 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'
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'
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
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)
795.77 m
(ii)
819.77 m
(iii)
834.77 m
(iv)
798.77 m
(v)
811.77 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 57° to 43°. 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'
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
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
(i)
79.74 m
(ii)
77.74 m
(iii)
82.74 m
(iv)
87.74 m
(v)
85.74 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 36° and 29° and the distance between them is 175 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'
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
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)
50.02 m
(ii)
60.02 m
(iii)
52.02 m
(iv)
55.02 m
(v)
58.02 m
Question
10
10.
A man in a boat rowing away from a lighthouse 100 m high, takes 1.5 min to change the angle of elevation of the top of the lighthouse from 45° to 37°. 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'
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'
45
1.0000
1.0035
1.0070
1.0105
1.0141
1.0176
1.0212
1.0247
1.0283
1.0319
6
12
18
24
30
(i)
2.36 m/sec
(ii)
7.36 m/sec
(iii)
8.36 m/sec
(iv)
0.36 m/sec
(v)
1.36 m/sec
Question
11
11.
Two vertical poles are on either side of a road. A 38 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 41°52' with the pole and when it is turned to rest against another pole, it makes an angle of 44°18' 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'
41
0.7547
0.7536
0.7524
0.7513
0.7501
0.7490
0.7478
0.7466
0.7455
0.7443
2
4
6
8
10
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
44
0.7193
0.7181
0.7169
0.7157
0.7145
0.7133
0.7120
0.7108
0.7096
0.7083
2
4
6
8
10
(i)
60.50 m
(ii)
55.50 m
(iii)
52.50 m
(iv)
50.50 m
(v)
58.50 m
Assignment Key
1) (v)
2) (v)
3) (iii)
4) (v)
5) (i)
6) (iv)
7) (v)
8) (iii)
9) (iv)
10) (iv)
11) (ii)
