ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Heights and Distances
Question 1
1.
The angles of depression of two boats from the top of a cliff 140 m high are 60° and 30° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
  • 306.33 m
  • 323.33 m
  • 348.33 m
  • 307.33 m
  • 331.33 m
Question 2
2.
    • A
    • tower
    • stands vertically on the ground.
    • From a point on the ground,
    • the angle of elevation
    • of the top of the
    • tower
    • is found to be
    • cos
      (-1)
       
      (
      3
      8
      )
    • .
    • If the distance between the point and the foot of the
    • tower
    • is
    • 190 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • tower
    • .
  • 523.67 m
  • 488.67 m
  • 514.67 m
  • 506.67 m
  • 482.67 m
Question 3
3.
    • A
    • chimney
    • stands vertically on the ground.
    • From a point on the ground,
    • the angle of elevation
    • of the top of the
    • chimney
    • is found to be
    • 60°
    • .
    • If the distance between the point and the top of the
    • chimney
    • is
    • 160 m
    • ,
    • find the height of the
    • chimney
    • .
  • 240
    m
  • 80

    √

    18
    m
  • 80
    m
  • 120

    √

    2
    m
  • 80

    √

    3
    m
Question 4
4.
    • A
    • building
    • stands vertically on the ground.
    • From a point on the ground,
    • the angle of elevation
    • of the top of the
    • building
    • is found to be
    • 30°
    • .
    • If the distance between the point and the top of the
    • building
    • is
    • 100 m
    • ,
    • find the distance between
    • the observation point and the foot of the
    • building
    • .
  • 50
    m
  • 75

    √

    2
    m
  • 50

    √

    3
    m
  • 150
    m
  • 50

    √

    18
    m
Question 5
5.
    • A tower stands vertically on the ground. From a point on the ground, the angle of elevation of the top of the tower is found to be 36°5'. If the distance between the observation point and the foot of the tower is 9 m, find the distance between the observation point and the top of the 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 Cosines
      x°
      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
  • 14.14 m
  • 6.14 m
  • 8.14 m
  • 11.14 m
  • 16.14 m
Question 6
6.
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 .
  • 7.99 m
  • 9.99 m
  • 12.99 m
  • 15.99 m
  • 17.99 m
Question 7
7.
    • Two poles of equal height are standing opposite to each other on either side of a road which is 15 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 31°50' and 27°30' respectively. Find the height of each pole and the distances of the point from the two poles .
    • From Table of Natural Tangents
      x°
      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
      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
      • height =
      • 5.25 m
      • , distances away =
      • 9.16 m
      • ,
      • 7.84 m
      • height =
      • 6.25 m
      • , distances away =
      • 10.16 m
      • ,
      • 8.84 m
      • height =
      • 3.25 m
      • , distances away =
      • 7.16 m
      • ,
      • 5.84 m
      • height =
      • 4.25 m
      • , distances away =
      • 8.16 m
      • ,
      • 6.84 m
      • height =
      • 2.25 m
      • , distances away =
      • 6.16 m
      • ,
      • 4.84 m
Question 8
8.
    • From the top of a 19 m high building , the angle of elevation of the top of a cable tower is 47°23' and the angle of depression of its foot is 23°37'. 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'
      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
    • 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
  • 63.23 m
  • 61.23 m
  • 66.23 m
  • 69.23 m
  • 71.23 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 45° and 30° and the distance between them is 180 m , find the height of the cliff.
  • 60.89 m
  • 62.89 m
  • 70.89 m
  • 68.89 m
  • 65.89 m
Question 10
10.
Two vertical poles are on either side of a road. A 39 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 60° with the pole and when it is turned to rest against another pole, it makes an angle of 30° with the road. Find the width of the road.
  • 58.27 m
  • 50.27 m
  • 56.27 m
  • 53.27 m
  • 48.27 m