ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Heights and Distances
Question 1
1.
From a point 160 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 60° and 45° respectively. Find the height of the cliff.
  • 132.00 m
  • 147.00 m
  • 175.00 m
  • 168.00 m
  • 160.00 m
Question 2
2.
    • 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
    • 45°
    • .
    • If the height of the
    • building
    • is
    • 110 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • building
    • .
  • 55

    √

    12
    m
  • 110

    √

    2
    m
  • 220

    √

    3
    m
  • 220
    m
  • 110
    m
Question 3
3.
The shadow of a vertical tower BA on a level ground is increased by 25 m, when the altitude of the sun changes from 60° to 45°. Find the height of the tower .
  • 64.15 m
  • 59.15 m
  • 56.15 m
  • 62.15 m
  • 54.15 m
Question 4
4.
An observer 1.3 m tall, is 170 m away from a tower . The angle of elevation of the top of the tower from her eyes is 30°. Find the height of the tower .
  • 99.46 m
  • 104.46 m
  • 102.46 m
  • 96.46 m
  • 94.46 m
Question 5
5.
    • A
    • tower
    • stands vertically on the ground.
    • The height of the
    • tower
    • is
    • 60
      m
    • .
    • The distance between the observation point and its foot
    • is
    • 60
      m
    • .
    • Find the angle of elevation.
  • 105°
  • 45°
  • 60°
  • 30°
  • 75°
Question 6
6.
Two boys are on opposite sides of a tower of 190 m height. They measure the angle of elevation of the top of the tower as 45° and 60° respectively. Find the distance between the two boys.
  • (
    95

    √

    6
    +
    95

    √

    2
    )
    m
  • (
    190
    +
    190
    3

    √

    3
    )
    m
  • (
    2
    +

    √

    3
    )
    m
  • (
    190

    √

    6
    +
    190
    3

    √

    18
    )
    m
  • 72200
    3
    m
Question 7
7.
    • There are two temples one on each bank of a river, just opposite to each other. One of the temples is 30 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30°2' and 43°27' respectively. Find the height of the other temple.
    • 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'
      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
  • 16.69 m
  • 8.69 m
  • 11.69 m
  • 6.69 m
  • 14.69 m
Question 8
8.
    • 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 55°38'. If the distance between the observation point and the foot of the radio tower is 17 m, find the distance between the observation point and the top of the radio 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 Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      55
      0.5736
      0.5721
      0.5707
      0.5693
      0.5678
      0.5664
      0.5650
      0.5635
      0.5621
      0.5606
      2
      5
      7
      9
      12
  • 33.12 m
  • 35.12 m
  • 25.12 m
  • 27.12 m
  • 30.12 m
Question 9
9.
    • 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
    • 45°
    • .
    • If the distance between the point and the foot of the
    • tower
    • is
    • 70 m
    • ,
    • find the height of the
    • tower
    • .
  • 70
    m
  • 69
    m
  • 73
    m
  • 68
    m
  • 71
    m
Question 10
10.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 120 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 60° respectively. Find the width of the river .
  • 69.28 m
  • 66.28 m
  • 72.28 m
  • 74.28 m
  • 64.28 m