ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Heights and Distances
Question 1
1.
From the top of a 11 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Find the height of the cable tower.
  • 27.05 m
  • 35.05 m
  • 25.05 m
  • 33.05 m
  • 30.05 m
Question 2
2.
The shadow of a vertical tower BA on a level ground is increased by 15 m, when the altitude of the sun changes from 60° to 30°. Find the height of the tower .
  • 9.99 m
  • 15.99 m
  • 17.99 m
  • 7.99 m
  • 12.99 m
Question 3
3.
    • A
    • radio tower
    • stands vertically on the ground.
    • From a point on the ground,
    • the angle of elevation
    • of the top of the
    • radio tower
    • is found to be
    • 60°
    • .
    • If the height of the
    • radio tower
    • is
    • 140 m
    • ,
    • find the distance between
    • the observation point and the foot of the
    • radio tower
    • .
  • 140
    m
  • 70

    √

    2
    m
  • 140
    3
    m
  • 140
    3

    √

    18
    m
  • 140
    3

    √

    3
    m
Question 4
4.
    • 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 48°23' with the pole and when it is turned to rest against another pole, it makes an angle of 49°46' 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'
      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
    • 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
  • 51.47 m
  • 43.47 m
  • 53.47 m
  • 48.47 m
  • 45.47 m
Question 5
5.
The angles of depression of two boats from the top of a cliff 70 m high are 45° and 60° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
  • 34.58 m
  • 24.58 m
  • 29.58 m
  • 26.58 m
  • 32.58 m
Question 6
6.
    • At the foot of a mountain, the elevation of its summit is 41°. After ascending 800 m towards the mountain up an incline of 27°, 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'
      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'
      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'
      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
      x°
      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
  • 785.54 m
  • 769.54 m
  • 761.54 m
  • 752.54 m
  • 781.54 m
Question 7
7.
    • From the top of a light house which is 85 m high from the sea level, the angles of depression of two ships are 30°28' and 27°45'. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
    • 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'
      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
  • 12.08 m
  • 20.08 m
  • 22.08 m
  • 14.08 m
  • 17.08 m
Question 8
8.
The angle of elevation of the top of a building from the foot of a tower is 45°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 60 m, find the height of the building .
  • 37.64 m
  • 31.64 m
  • 34.64 m
  • 29.64 m
  • 39.64 m
Question 9
9.
    • There are two temples one on each bank of a river, just opposite to each other. One of the temples is 110 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 39°19' and 46°54' respectively. Find the width of the river .
    • 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
    • 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
  • 118.94 m
  • 102.94 m
  • 84.94 m
  • 119.94 m
  • 97.94 m
Question 10
10.
    • From the top of a 19 m high building , the angle of elevation of the top of a cable tower is 30°50' and the angle of depression of its foot is 28°35'. Find the height of the cable tower.
    • 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'
      28
      0.5317
      0.5340
      0.5362
      0.5384
      0.5407
      0.5430
      0.5452
      0.5475
      0.5498
      0.5520
      4
      8
      11
      15
      19
  • 36.81 m
  • 34.81 m
  • 44.81 m
  • 42.81 m
  • 39.81 m