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 50 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 33°5' and 21°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'
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'
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
(i)
16.96 m
(ii)
14.96 m
(iii)
22.96 m
(iv)
19.96 m
(v)
24.96 m
Question
2
2.
From a point 200 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 26°5' and 25°47' 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'
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'
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
(i)
9.28 m
(ii)
3.28 m
(iii)
2.28 m
(iv)
0.28 m
(v)
1.28 m
Question
3
3.
The angles of depression of two boats from the top of a cliff 160 m high are 29° and 40° 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'
61
1.8040
1.8115
1.8190
1.8265
1.8341
1.8418
1.8495
1.8572
1.8650
1.8728
13
26
38
51
64
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)
94.95 m
(ii)
100.95 m
(iii)
102.95 m
(iv)
92.95 m
(v)
97.95 m
Question
4
4.
The angles of depression of two boats from the top of a cliff 190 m high are 29° and 21° 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'
61
1.8040
1.8115
1.8190
1.8265
1.8341
1.8418
1.8495
1.8572
1.8650
1.8728
13
26
38
51
64
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
(i)
837.73 m
(ii)
825.73 m
(iii)
852.73 m
(iv)
833.73 m
(v)
855.73 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 25° to 48°, 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'
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'
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)
2 min 36 sec
(ii)
4 min 38 sec
(iii)
1 min 35 sec
(iv)
3 min 37 sec
(v)
6 min 40 sec
Question
6
6.
From a point 170 m above a lake, the angle of elevation of a cloud is 26° and the angle of depression of its reflection in the lake is 58°. 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'
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'
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)
313.04 m
(ii)
291.04 m
(iii)
334.04 m
(iv)
346.04 m
(v)
319.04 m
Question
7
7.
At the foot of a mountain, the elevation of its summit is 41°. After ascending 700 m towards the mountain up an incline of 28°, 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'
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
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 Sines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
28
0.4695
0.4710
0.4726
0.4741
0.4756
0.4772
0.4787
0.4802
0.4818
0.4833
3
5
9
10
13
(i)
706.41 m
(ii)
654.41 m
(iii)
686.41 m
(iv)
673.41 m
(v)
679.41 m
Question
8
8.
The shadow of a vertical tower BA on a level ground is increased by 40 m, when the altitude of the sun changes from 59° to 37°. 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
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)
58.09 m
(ii)
55.09 m
(iii)
50.09 m
(iv)
60.09 m
(v)
52.09 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 34° and 37° and the distance between them is 165 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'
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 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)
63.73 m
(ii)
61.73 m
(iii)
53.73 m
(iv)
58.73 m
(v)
55.73 m
Question
10
10.
A man in a boat rowing away from a lighthouse 75 m high, takes 3 min to change the angle of elevation of the top of the lighthouse from 37° to 36°. 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'
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'
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)
8.02 m/sec
(ii)
0.02 m/sec
(iii)
1.02 m/sec
(iv)
2.02 m/sec
(v)
7.02 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 49°37' with the pole and when it is turned to rest against another pole, it makes an angle of 47°25' 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'
49
0.6561
0.6547
0.6534
0.6521
0.6508
0.6494
0.6481
0.6468
0.6455
0.6441
2
4
7
9
11
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
47
0.6820
0.6807
0.6794
0.6784
0.6769
0.6756
0.6743
0.6730
0.6717
0.6704
2
4
6
9
11
(i)
41.06 m
(ii)
44.06 m
(iii)
36.06 m
(iv)
38.06 m
(v)
46.06 m
Assignment Key
1) (iv)
2) (v)
3) (v)
4) (i)
5) (iv)
6) (v)
7) (v)
8) (ii)
9) (iv)
10) (ii)
11) (i)
