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 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°47' and 26°23' 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'
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'
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)
29.72 m
(ii)
34.72 m
(iii)
37.72 m
(iv)
31.72 m
(v)
39.72 m
Question
2
2.
From a point 80 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°39' and 33°42' 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'
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'
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)
31.49 m
(ii)
28.49 m
(iii)
33.49 m
(iv)
25.49 m
(v)
23.49 m
Question
3
3.
The angles of depression of two boats from the top of a cliff 120 m high are 31° and 37° 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'
59
1.6643
1.6709
1.6775
1.6842
1.6909
1.6977
1.7045
1.7113
1.7182
1.7251
11
23
34
45
56
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
53
1.3270
1.3319
1.3367
1.3416
1.3465
1.3514
1.3564
1.3613
1.3663
1.3713
8
16
25
33
41
(i)
40.48 m
(ii)
37.48 m
(iii)
35.48 m
(iv)
45.48 m
(v)
43.48 m
Question
4
4.
The angles of depression of two boats from the top of a cliff 110 m high are 24° and 32° 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'
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 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)
411.09 m
(ii)
439.09 m
(iii)
423.09 m
(iv)
450.09 m
(v)
395.09 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 23° 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'
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'
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)
14 min 4 sec
(ii)
13 min 8 sec
(iii)
17 min 12 sec
(iv)
12 min 6 sec
(v)
15 min 10 sec
Question
6
6.
From a point 90 m above a lake, the angle of elevation of a cloud is 33° 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'
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'
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)
179.93 m
(ii)
202.93 m
(iii)
184.93 m
(iv)
161.93 m
(v)
208.93 m
Question
7
7.
At the foot of a mountain, the elevation of its summit is 50°. After ascending 1000 m towards the mountain up an incline of 26°, 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'
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'
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'
26
0.8988
0.8980
0.8973
0.8965
0.8957
0.8949
0.8942
0.8934
0.8926
0.8918
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'
26
0.4384
0.4399
0.4415
0.4431
0.4446
0.4462
0.4478
0.4493
0.4509
0.4524
3
5
8
11
13
(i)
2195.69 m
(ii)
2015.69 m
(iii)
1925.69 m
(iv)
2385.69 m
(v)
2165.69 m
Question
8
8.
The shadow of a vertical tower BA on a level ground is increased by 25 m, when the altitude of the sun changes from 48° to 22°. 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'
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
(i)
12.87 m
(ii)
18.87 m
(iii)
10.87 m
(iv)
15.87 m
(v)
20.87 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 45° and the distance between them is 190 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'
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)
76.65 m
(ii)
78.65 m
(iii)
81.65 m
(iv)
86.65 m
(v)
84.65 m
Question
10
10.
A man in a boat rowing away from a lighthouse 30 m high, takes 4.5 min to change the angle of elevation of the top of the lighthouse from 32° to 31°. 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'
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'
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)
1.01 m/sec
(ii)
8.01 m/sec
(iii)
0.01 m/sec
(iv)
7.01 m/sec
(v)
2.01 m/sec
Question
11
11.
Two vertical poles are on either side of a road. A 31 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 29°59' with the pole and when it is turned to rest against another pole, it makes an angle of 25°30' 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'
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
(i)
57.83 m
(ii)
54.83 m
(iii)
49.83 m
(iv)
51.83 m
(v)
59.83 m
Assignment Key
1) (ii)
2) (ii)
3) (i)
4) (iii)
5) (i)
6) (iii)
7) (v)
8) (iv)
9) (iii)
10) (iii)
11) (ii)
