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 49°39' and 21°1' 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'
21
0.3839
0.3859
0.3879
0.3899
0.3919
0.3939
0.3959
0.3979
0.4000
0.4020
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'
49
1.1504
1.1544
1.1585
1.1626
1.1667
1.1708
1.1750
1.1792
1.1833
1.1875
7
14
21
27
34
(i)
54.95 m
(ii)
52.95 m
(iii)
44.95 m
(iv)
49.95 m
(v)
46.95 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 48°11' and 45°34' 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'
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
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
(i)
9.82 m
(ii)
8.82 m
(iii)
7.82 m
(iv)
5.82 m
(v)
6.82 m
Question
3
3.
The angles of depression of two boats from the top of a cliff 180 m high are 38° 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'
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
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)
63.31 m
(ii)
73.31 m
(iii)
71.31 m
(iv)
65.31 m
(v)
68.31 m
Question
4
4.
The angles of depression of two boats from the top of a cliff 130 m high are 30° and 36° 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'
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
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
(i)
392.11 m
(ii)
417.11 m
(iii)
404.11 m
(iv)
410.11 m
(v)
381.11 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 22° to 43°, 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'
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)
7 min 38 sec
(ii)
8 min 39 sec
(iii)
10 min 41 sec
(iv)
4 min 36 sec
(v)
6 min 37 sec
Question
6
6.
From a point 150 m above a lake, the angle of elevation of a cloud is 35° 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'
35
0.7002
0.7028
0.7054
0.7080
0.7107
0.7133
0.7159
0.7186
0.7212
0.7239
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'
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)
305.94 m
(ii)
312.94 m
(iii)
327.94 m
(iv)
343.94 m
(v)
344.94 m
Question
7
7.
At the foot of a mountain, the elevation of its summit is 40°. After ascending 1000 m towards the mountain up an incline of 27°, the elevation changes to 65°. 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'
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'
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
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)
940.33 m
(ii)
913.33 m
(iii)
918.33 m
(iv)
949.33 m
(v)
936.33 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 60° to 47°. 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'
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
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)
98.55 m
(ii)
93.55 m
(iii)
101.55 m
(iv)
95.55 m
(v)
103.55 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 22° and 49° and the distance between them is 195 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'
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'
49
1.1504
1.1544
1.1585
1.1626
1.1667
1.1708
1.1750
1.1792
1.1833
1.1875
7
14
21
27
34
(i)
61.30 m
(ii)
55.30 m
(iii)
58.30 m
(iv)
53.30 m
(v)
63.30 m
Question
10
10.
A man in a boat rowing away from a lighthouse 30 m high, takes 0.5 min to change the angle of elevation of the top of the lighthouse from 46° to 35°. 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'
35
0.7002
0.7028
0.7054
0.7080
0.7107
0.7133
0.7159
0.7186
0.7212
0.7239
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'
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
(i)
7.46 m/sec
(ii)
2.46 m/sec
(iii)
0.46 m/sec
(iv)
1.46 m/sec
(v)
8.46 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 36°15' with the pole and when it is turned to rest against another pole, it makes an angle of 40°19' 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'
36
0.8090
0.8080
0.8070
0.8059
0.8049
0.8039
0.8028
0.8018
0.8007
0.7997
2
3
5
7
8
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
40
0.7660
0.7649
0.7638
0.7627
0.7615
0.7604
0.7593
0.7581
0.7570
0.7559
2
4
6
7
9
(i)
48.64 m
(ii)
53.64 m
(iii)
51.64 m
(iv)
45.64 m
(v)
43.64 m
Assignment Key
1) (iv)
2) (iii)
3) (v)
4) (iii)
5) (i)
6) (iii)
7) (v)
8) (i)
9) (iii)
10) (iii)
11) (i)
