ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Heights and Distances
Question 1
1.
    • 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
    • cot
      (-1)
       
      (
      1
      2
      )
    • .
    • If the distance between the point and the foot of the
    • tower
    • is
    • 50 m
    • ,
    • find the height of the
    • tower
    • .
  • 128.00 m
  • 105.00 m
  • 87.00 m
  • 96.00 m
  • 100.00 m
Question 2
2.
    • From a point 200 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 46°12' and 39°2' respectively. Find the height of the cliff.
    • 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
  • 165.16 m
  • 134.16 m
  • 162.16 m
  • 157.16 m
  • 180.16 m
Question 3
3.
    • A pole stands vertically on the ground. From a point on the ground, the angle of elevation of the top of the pole is found to be 31°57'. If the height of the pole is 14 m, find the distance between the observation point and the top of the pole.
    • 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 Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      31
      0.5150
      0.5165
      0.5780
      0.5195
      0.5210
      0.5225
      0.5240
      0.5255
      0.5270
      0.5284
      2
      5
      7
      10
      12
  • 26.46 m
  • 31.46 m
  • 21.46 m
  • 23.46 m
  • 29.46 m
Question 4
4.
A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 45° and the angle of elevation of the top of the building is 30°. If the height of the building is 6 m, find the height of the flag staff .
  • 3.39 m
  • 4.39 m
  • 6.39 m
  • 2.39 m
  • 5.39 m
Question 5
5.
The angles of depression of two boats from the top of a cliff 200 m high are 45° and 60° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
  • 315.48 m
  • 288.48 m
  • 329.48 m
  • 301.48 m
  • 330.48 m
Question 6
6.
    • There are two temples one on each bank of a river, just opposite to each other. One of the temples is 50 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 31°21' and 43°46' 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'
      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'
      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
  • 55.20 m
  • 52.20 m
  • 47.20 m
  • 49.20 m
  • 57.20 m
Question 7
7.
From the top of a 18 m high building , the angle of elevation of the top of a cable tower is 45° and the angle of depression of its foot is 30°. Find the height of the cable tower.
  • 52.17 m
  • 54.17 m
  • 49.17 m
  • 46.17 m
  • 44.17 m
Question 8
8.
Two boys are on opposite sides of a tower of 70 m height. They measure the angle of elevation of the top of the tower as 60° and 45° respectively. Find the distance between the two boys.
  • (
    70
    3

    √

    18
    +
    70

    √

    6
    )
    m
  • (
    70
    3

    √

    3
    +
    70
    )
    m
  • (
    −
    9800
    3
    )
    m
  • (
    −
    2
    −

    √

    3
    )
    m
  • (
    35

    √

    2
    +
    35

    √

    6
    )
    m
Question 9
9.
A man 1.6 m tall stands at a distance of 7.8 m from a lamp post and casts a shadow of 9.1 m on the ground. Find the height of the lamp post .
  • 2.97 m
  • 3.97 m
  • 4.97 m
  • 0.97 m
  • 1.97 m
Question 10
10.
    • 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 foot of the
    • building
    • is
    • 160 m
    • ,
    • find the height of the
    • building
    • .
  • 160
    m
  • 160
    3

    √

    3
    m
  • 160
    3
    m
  • 80

    √

    2
    m
  • 160
    3

    √

    18
    m