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
      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
      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
      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
      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
      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
      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
      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
      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
      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'
      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
      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
      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
      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
      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
      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
      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
      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
      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
      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'
      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
      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
      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
      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
      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)