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 110 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°49' and 22°39' 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'
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'
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)
40.90 m
(ii)
45.90 m
(iii)
42.90 m
(iv)
50.90 m
(v)
48.90 m
Question
2
2.
From a point 150 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 30°24' and 21°21' 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'
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'
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
(i)
29.37 m
(ii)
34.37 m
(iii)
26.37 m
(iv)
24.37 m
(v)
32.37 m
Question
3
3.
The angles of depression of two boats from the top of a cliff 120 m high are 48° and 35° 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'
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'
55
1.4281
1.4335
1.4388
1.4442
1.4496
1.4550
1.4605
1.4659
1.4715
1.4770
9
18
27
36
45
(i)
63.32 m
(ii)
66.32 m
(iii)
68.32 m
(iv)
60.32 m
(v)
58.32 m
Question
4
4.
The angles of depression of two boats from the top of a cliff 170 m high are 21° and 50° 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'
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
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
(i)
563.51 m
(ii)
567.51 m
(iii)
601.51 m
(iv)
585.51 m
(v)
612.51 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 8 min for the angle of depression to change from 29° to 33°, 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'
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
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)
47 min 39 sec
(ii)
46 min 38 sec
(iii)
49 min 41 sec
(iv)
43 min 35 sec
(v)
45 min 37 sec
Question
6
6.
From a point 50 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 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'
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'
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)
101.36 m
(ii)
96.36 m
(iii)
99.36 m
(iv)
93.36 m
(v)
91.36 m
Question
7
7.
At the foot of a mountain, the elevation of its summit is 43°. After ascending 1000 m towards the mountain up an incline of 26°, the elevation changes to 63°. 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'
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 Tangents
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
63
1.9626
1.9711
1.9797
1.9883
1.9970
2.0057
2.0145
2.0233
2.0323
2.0413
15
29
44
58
73
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)
1019.96 m
(ii)
1199.96 m
(iii)
1169.96 m
(iv)
1479.96 m
(v)
1259.96 m
Question
8
8.
The shadow of a vertical tower BA on a level ground is increased by 10 m, when the altitude of the sun changes from 55° 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'
55
1.4281
1.4335
1.4388
1.4442
1.4496
1.4550
1.4605
1.4659
1.4715
1.4770
9
18
27
36
45
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)
20.96 m
(ii)
18.96 m
(iii)
12.96 m
(iv)
15.96 m
(v)
10.96 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 49° and 25° and the distance between them is 115 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'
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
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
(i)
38.16 m
(ii)
33.16 m
(iii)
41.16 m
(iv)
35.16 m
(v)
43.16 m
Question
10
10.
A man in a boat rowing away from a lighthouse 25 m high, takes 3 min to change the angle of elevation of the top of the lighthouse from 47° 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'
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)
1.06 m/sec
(ii)
7.06 m/sec
(iii)
2.06 m/sec
(iv)
8.06 m/sec
(v)
0.06 m/sec
Question
11
11.
Two vertical poles are on either side of a road. A 28 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 37°56' with the pole and when it is turned to rest against another pole, it makes an angle of 34°2' 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'
37
0.7986
0.7976
0.7963
0.7955
0.7944
0.7934
0.7923
0.7912
0.7902
0.7891
2
4
5
7
9
From Table of Natural Cosines
x°
0'
6'
12'
18'
24'
30'
36'
42'
48'
54'
1'
2'
3'
4'
5'
34
0.8290
0.8281
0.8271
0.8261
0.8251
0.8241
0.8231
0.8221
0.8211
0.8202
2
3
5
7
8
(i)
50.29 m
(ii)
45.29 m
(iii)
40.29 m
(iv)
42.29 m
(v)
48.29 m
Assignment Key
1) (ii)
2) (i)
3) (i)
4) (iv)
5) (ii)
6) (ii)
7) (ii)
8) (iv)
9) (i)
10) (v)
11) (ii)
