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 140 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 39°15' and 23°17' 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'
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'
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)
55.24 m
(ii)
63.24 m
(iii)
65.24 m
(iv)
60.24 m
(v)
57.24 m
Question
2
2.
From a point 60 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 50°25' and 30°38' 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'
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 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)
37.04 m
(ii)
32.04 m
(iii)
34.04 m
(iv)
42.04 m
(v)
40.04 m
Question
3
3.
The angles of depression of two boats from the top of a cliff 100 m high are 44° 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'
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'
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)
10.63 m
(ii)
20.63 m
(iii)
12.63 m
(iv)
18.63 m
(v)
15.63 m
Question
4
4.
The angles of depression of two boats from the top of a cliff 180 m high are 23° and 48° 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'
67
2.3559
2.3673
2.3789
2.3906
2.4023
2.4142
2.4262
2.4383
2.4504
2.4627
20
40
60
79
99
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)
591.13 m
(ii)
609.13 m
(iii)
570.13 m
(iv)
584.13 m
(v)
586.13 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 14 min for the angle of depression to change from 36° 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'
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'
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)
72 min 15 sec
(ii)
68 min 11 sec
(iii)
71 min 14 sec
(iv)
74 min 16 sec
(v)
70 min 13 sec
Question
6
6.
From a point 160 m above a lake, the angle of elevation of a cloud is 34° and the angle of depression of its reflection in the lake is 64°. 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'
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'
64
2.0503
2.0594
2.0686
2.0778
2.0872
2.0965
2.1060
2.1155
2.1251
2.1348
16
31
47
63
78
(i)
321.88 m
(ii)
312.88 m
(iii)
293.88 m
(iv)
316.88 m
(v)
329.88 m
Question
7
7.
At the foot of a mountain, the elevation of its summit is 46°. After ascending 500 m towards the mountain up an incline of 25°, the elevation changes to 67°. 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'
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'
67
2.3559
2.3673
2.3789
2.3906
2.4023
2.4142
2.4262
2.4383
2.4504
2.4627
20
40
60
79
99
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)
655.54 m
(ii)
654.54 m
(iii)
673.54 m
(iv)
671.54 m
(v)
684.54 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 52° to 29°. 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'
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'
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)
31.22 m
(ii)
34.22 m
(iii)
37.22 m
(iv)
29.22 m
(v)
39.22 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 48° and 29° and the distance between them is 215 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'
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'
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)
84.50 m
(ii)
79.50 m
(iii)
76.50 m
(iv)
82.50 m
(v)
74.50 m
Question
10
10.
A man in a boat rowing away from a lighthouse 30 m high, takes 3.5 min to change the angle of elevation of the top of the lighthouse from 44° to 38°. 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'
38
0.7813
0.7841
0.7869
0.7898
0.7926
0.7954
0.7983
0.8012
0.8040
0.8069
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'
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)
2.03 m/sec
(ii)
8.03 m/sec
(iii)
1.03 m/sec
(iv)
7.03 m/sec
(v)
0.03 m/sec
Question
11
11.
Two vertical poles are on either side of a road. A 37 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 33°49' with the pole and when it is turned to rest against another pole, it makes an angle of 49°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'
33
0.8387
0.8377
0.8368
0.8358
0.8348
0.8339
0.8329
0.8320
0.8310
0.8300
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'
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
(i)
59.86 m
(ii)
54.86 m
(iii)
51.86 m
(iv)
57.86 m
(v)
49.86 m
Assignment Key
1) (iv)
2) (i)
3) (v)
4) (v)
5) (iii)
6) (iv)
7) (iv)
8) (ii)
9) (ii)
10) (v)
11) (ii)
