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 37°37' and 27°19' respectively. Find the height of the cliff.
    • From Table of Natural Tangents
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      27
      0.5095
      0.5117
      0.5139
      0.5161
      0.5184
      0.5206
      0.5228
      0.5250
      0.5272
      0.5295
      4
      7
      11
      15
      18
    • From Table of Natural Tangents
      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)
    64.14 m
  • (ii)
    62.14 m
  • (iii)
    70.14 m
  • (iv)
    67.14 m
  • (v)
    72.14 m
Question 2
2.
    • From a point 70 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°9' and 39°4' respectively. Find the height of the pillar.
    • From Table of Natural Tangents
      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
      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)
    30.05 m
  • (ii)
    32.05 m
  • (iii)
    24.05 m
  • (iv)
    22.05 m
  • (v)
    27.05 m
Question 3
3.
    • The angles of depression of two boats from the top of a cliff 130 m high are 22° 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
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      68
      2.4751
      2.4876
      2.5002
      2.5129
      2.5257
      2.5386
      2.5517
      2.5679
      2.5782
      2.5916
      22
      43
      65
      87
      108
    • From Table of Natural Tangents
      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)
    177.71 m
  • (ii)
    212.71 m
  • (iii)
    204.71 m
  • (iv)
    202.71 m
  • (v)
    220.71 m
Question 4
4.
    • The angles of depression of two boats from the top of a cliff 140 m high are 49° and 46° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
    • From Table of Natural Tangents
      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
      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)
    238.90 m
  • (ii)
    256.90 m
  • (iii)
    251.90 m
  • (iv)
    270.90 m
  • (v)
    269.90 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 13 min for the angle of depression to change from 22° to 27°, how soon after this, will the car reach the observation tower?
    • From Table of Natural Tangents
      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
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      27
      0.5095
      0.5117
      0.5139
      0.5161
      0.5184
      0.5206
      0.5228
      0.5250
      0.5272
      0.5295
      4
      7
      11
      15
      18
  • (i)
    51 min 49 sec
  • (ii)
    48 min 46 sec
  • (iii)
    50 min 48 sec
  • (iv)
    49 min 47 sec
  • (v)
    47 min 45 sec
Question 6
6.
    • From a point 150 m above a lake, the angle of elevation of a cloud is 31° 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
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      31
      0.6009
      0.6032
      0.6056
      0.6080
      0.6104
      0.6128
      0.6152
      0.6176
      0.6200
      0.6224
      4
      8
      12
      16
      20
    • From Table of Natural Tangents
      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)
    297.86 m
  • (ii)
    277.86 m
  • (iii)
    276.86 m
  • (iv)
    290.86 m
  • (v)
    318.86 m
Question 7
7.
    • At the foot of a mountain, the elevation of its summit is 41°. After ascending 600 m towards the mountain up an incline of 25°, the elevation changes to 64°. Find the height of the mountain.
    • From Table of Natural Tangents
      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
      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
    • From Table of Natural Cosines
      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
      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)
    658.97 m
  • (ii)
    633.97 m
  • (iii)
    639.97 m
  • (iv)
    607.97 m
  • (v)
    626.97 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 56° to 36°. Find the height of the tower .
    • From Table of Natural Tangents
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      56
      1.4826
      1.4882
      1.4938
      1.4994
      1.5051
      1.5108
      1.5166
      1.5224
      1.5282
      1.5340
      10
      19
      29
      38
      48
    • From Table of Natural Tangents
      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
  • (i)
    44.86 m
  • (ii)
    46.86 m
  • (iii)
    54.86 m
  • (iv)
    52.86 m
  • (v)
    49.86 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 42° and 29° and the distance between them is 185 m , find the height of the cliff.
    • From Table of Natural Tangents
      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
      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)
    58.47 m
  • (ii)
    60.47 m
  • (iii)
    63.47 m
  • (iv)
    68.47 m
  • (v)
    66.47 m
Question 10
10.
    • A man in a boat rowing away from a lighthouse 90 m high, takes 2.5 min to change the angle of elevation of the top of the lighthouse from 36° to 25°. Find the speed of the boat.
    • From Table of Natural Tangents
      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
      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
  • (i)
    1.46 m/sec
  • (ii)
    0.46 m/sec
  • (iii)
    8.46 m/sec
  • (iv)
    7.46 m/sec
  • (v)
    2.46 m/sec
Question 11
11.
    • Two vertical poles are on either side of a road. A 22 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 28°54' with the pole and when it is turned to rest against another pole, it makes an angle of 48°28' with the road. Find the width of the road.
    • From Table of Natural Cosines
      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 Cosines
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      48
      0.6691
      0.6678
      0.6665
      0.6652
      0.6639
      0.6626
      0.6613
      0.6600
      0.6587
      0.6574
      2
      4
      7
      9
      11
  • (i)
    30.85 m
  • (ii)
    36.85 m
  • (iii)
    38.85 m
  • (iv)
    28.85 m
  • (v)
    33.85 m
    Assignment Key

  •  1) (iv)
  •  2) (v)
  •  3) (iii)
  •  4) (ii)
  •  5) (iv)
  •  6) (iv)
  •  7) (ii)
  •  8) (v)
  •  9) (iii)
  •  10) (ii)
  •  11) (v)