EduSahara™ Assignment
Name : Heights and Distances using Tables
Chapter : Heights and Distances
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
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 34°16'. If the height of the radio tower is 3 m, find the distance between the observation point and the top of the radio tower.
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 Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
34
0.5592
0.5606
0.5621
0.5635
0.5650
0.5664
0.5678
0.5693
0.5707
0.5721
2
5
7
9
12
(i)
6.33 m
(ii)
4.33 m
(iii)
5.33 m
(iv)
3.33 m
(v)
7.33 m
Question
2
2.
A pole stands vertically on the ground. From a point on the ground, the angle of elevation of the top of the pole is found to be 30°48'. If the height of the pole is 12 m, find the distance between the observation point and the foot of the pole.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
30
0.5774
0.5797
0.5820
0.5844
0.5867
0.5890
0.5914
0.5938
0.5961
0.5985
4
8
12
16
20
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)
23.13 m
(ii)
15.13 m
(iii)
20.13 m
(iv)
17.13 m
(v)
25.13 m
Question
3
3.
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 46°46'. If the distance between the observation point and the foot of the radio tower is 13 m, find the distance between the observation point and the top of the radio tower.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
46
1.0355
1.0392
1.0428
1.0464
1.0501
1.0538
1.0575
1.0612
1.0649
1.0686
6
12
18
25
31
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
46
0.6947
0.6934
0.6921
0.6909
0.6896
0.6884
0.6871
0.6858
0.6845
0.6833
2
4
6
9
11
(i)
13.98 m
(ii)
15.98 m
(iii)
21.98 m
(iv)
23.98 m
(v)
18.98 m
Question
4
4.
A pole stands vertically on the ground. From a point on the ground, the angle of elevation of the top of the pole is found to be 43°46'. If the distance between the observation point and the foot of the pole is 7 m, find the height of the pole.
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)
7.70 m
(ii)
5.70 m
(iii)
8.70 m
(iv)
4.70 m
(v)
6.70 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 42°49'. If the distance between the observation point and the top of the chimney is 4 m, find the height of the chimney.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
42
0.6691
0.6704
0.6717
0.6730
0.6743
0.6756
0.6769
0.6782
0.6794
0.6807
2
4
6
9
11
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
42
0.7431
0.7420
0.7408
0.7396
0.7385
0.7373
0.7361
0.7349
0.7337
0.7325
2
4
6
8
10
(i)
4.72 m
(ii)
3.72 m
(iii)
1.72 m
(iv)
0.72 m
(v)
2.72 m
Question
6
6.
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 39°59'. If the distance between the observation point and the top of the tower is 1 m, find the distance between the observation point and the foot of the tower.
From Table of Natural Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
39
0.6293
0.6307
0.6320
0.6334
0.6347
0.6361
0.6374
0.6388
0.6401
0.6414
2
5
7
9
12
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
39
0.7771
0.7760
0.7749
0.7738
0.7727
0.7216
0.7705
0.7694
0.7683
0.7672
2
4
6
7
9
(i)
2.77 m
(ii)
0.77 m
(iii)
8.77 m
(iv)
1.77 m
(v)
7.77 m
Question
7
7.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 43°41' with the ground. The top of the tree touches the ground at a distance of 190 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)
462.19 m
(ii)
444.19 m
(iii)
432.19 m
(iv)
461.19 m
(v)
428.19 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 130 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 46°51' and 58°7' 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'
46
1.0355
1.0392
1.0428
1.0464
1.0501
1.0538
1.0575
1.0612
1.0649
1.0686
6
12
18
25
31
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)
80.86 m
(ii)
75.86 m
(iii)
83.86 m
(iv)
85.86 m
(v)
77.86 m
Question
9
9.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 50 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 36°17' and 52°14' respectively. Find the height of the other temple.
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'
52
1.2799
1.2846
1.2892
1.2938
1.2985
1.3032
1.3079
1.3127
1.3175
1.3222
8
16
24
31
39
(i)
16.56 m
(ii)
18.56 m
(iii)
26.56 m
(iv)
24.56 m
(v)
21.56 m
Question
10
10.
An observer 1.6 m tall, is 170 m away from a tower . The angle of elevation of the top of the tower from her eyes is 59°28'. 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'
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
(i)
275.82 m
(ii)
281.82 m
(iii)
312.82 m
(iv)
289.82 m
(v)
292.82 m
Question
11
11.
An aeroplane is flying horizontally 1500 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 45°. After 50 sec , its elevation from the same point changes to 23°. 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'
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'
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)
164.42 kmph
(ii)
133.42 kmph
(iii)
146.42 kmph
(iv)
141.42 kmph
Question
12
12.
Two poles of equal height are standing opposite to each other on either side of a road which is 15 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 23°51' and 29°17' respectively. Find the height of each pole and the distances of the point from the two poles .
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'
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)
height =
1.71 m
, distances away =
4.61 m
,
6.39 m
(ii)
height =
5.71 m
, distances away =
8.61 m
,
10.39 m
(iii)
height =
4.71 m
, distances away =
7.61 m
,
9.39 m
(iv)
height =
3.71 m
, distances away =
6.61 m
,
8.39 m
(v)
height =
2.71 m
, distances away =
5.61 m
,
7.39 m
Question
13
13.
From the top of a light house which is 85 m high from the sea level, the angles of depression of two ships are 50°18' and 37°13'. 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'
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'
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)
44.35 m
(ii)
46.35 m
(iii)
36.35 m
(iv)
41.35 m
(v)
38.35 m
Question
14
14.
From the top of a 19 m high building , the angle of elevation of the top of a cable tower is 46°3' and the angle of depression of its foot is 45°26'. Find the height of the cable tower.
From Table of Natural Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
46
1.0355
1.0392
1.0428
1.0464
1.0501
1.0538
1.0575
1.0612
1.0649
1.0686
6
12
18
25
31
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)
43.41 m
(ii)
33.41 m
(iii)
41.41 m
(iv)
35.41 m
(v)
38.41 m
Question
15
15.
The angle of elevation of the top of a building from the foot of a tower is 42°20'. The angle of elevation of the top of the tower from the foot of the building is 39°6'. If the height of the tower is 95 m, find the height of the building .
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'
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)
101.49 m
(ii)
84.49 m
(iii)
134.49 m
(iv)
109.49 m
(v)
106.49 m
Question
16
16.
A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 29°47' and the angle of elevation of the top of the building is 26°36'. If the height of the building is 8 m, find the height of the flag staff .
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'
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)
3.14 m
(ii)
9.14 m
(iii)
1.14 m
(iv)
0.14 m
(v)
2.14 m
Question
17
17.
A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 44°57' and the angle of elevation of the top of the building is 39°56'. If the height of the flag staff is 20 m, find the height of the building .
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'
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)
75.92 m
(ii)
103.92 m
(iii)
120.92 m
(iv)
91.92 m
(v)
117.92 m
Assignment Key
1) (iii)
2) (iii)
3) (v)
4) (v)
5) (v)
6) (ii)
7) (ii)
8) (i)
9) (v)
10) (iv)
11) (iii)
12) (iv)
13) (iv)
14) (v)
15) (v)
16) (iii)
17) (ii)
