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
    • cos
      (-1)
       
      (
      1
      2
      )
    • .
    • If the distance between the point and the foot of the
    • tower
    • is
    • 100 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • tower
    • .
  • 184.00 m
  • 212.00 m
  • 213.00 m
  • 200.00 m
  • 198.00 m
Question 2
2.
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 60° and the angle of elevation of the top of the building is 30°. If the height of the building is 15 m, find the height of the flag staff .
  • 33.00 m
  • 30.00 m
  • 27.00 m
  • 25.00 m
  • 35.00 m
Question 3
3.
A person, walking 35 m from a point toward a flagpost , observes that its angle of elevation changes from 45° to 60°. Find the height of the flagpost .
  • (
    105
    4

    √

    6
    +
    105
    4

    √

    2
    )
    m
  • 3675
    2
    m
  • (
    105
    2
    +
    35
    2

    √

    3
    )
    m
  • (
    2
    +

    √

    3
    )
    m
  • (
    105
    2

    √

    6
    +
    35
    2

    √

    18
    )
    m
Question 4
4.
    • 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 41°24' and 21°10' respectively. Find the height of the pillar.
    • From Table of Natural Tangents
      x°
      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
      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
  • 79.10 m
  • 84.10 m
  • 82.10 m
  • 74.10 m
  • 76.10 m
Question 5
5.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 180 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 45° respectively. Find the width of the river .
  • 180.00 m
  • 177.00 m
  • 195.00 m
  • 168.00 m
  • 196.00 m
Question 6
6.
From the top of a 12 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.
  • 27.78 m
  • 29.78 m
  • 35.78 m
  • 37.78 m
  • 32.78 m
Question 7
7.
    • 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
    • 30°
    • .
    • If the height of the
    • radio tower
    • is
    • 130 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • radio tower
    • .
  • 258
    m
  • 262
    m
  • 260
    m
  • 261
    m
  • 259
    m
Question 8
8.
Two boys are on opposite sides of a tower of 150 m height. They measure the angle of elevation of the top of the tower as 30° and 45° respectively. Find the distance between the two boys.
  • (
    2
    +

    √

    3
    )
    m
  • (
    150

    √

    3
    +
    150
    )
    m
  • (
    150

    √

    18
    +
    150

    √

    6
    )
    m
  • (
    225

    √

    2
    +
    75

    √

    6
    )
    m
  • 45000
    m
Question 9
9.
    • The angles of depression of two boats from the top of a cliff 50 m high are 37° and 38° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      53
      1.3270
      1.3319
      1.3367
      1.3416
      1.3465
      1.3514
      1.3564
      1.3613
      1.3663
      1.3713
      8
      16
      25
      33
      41
    • From Table of Natural Tangents
      x°
      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
  • 2.36 m
  • 3.36 m
  • 0.36 m
  • 4.36 m
  • 1.36 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 height of the
    • building
    • is
    • 50 m
    • ,
    • find the distance between
    • the observation point and the foot of the
    • building
    • .
  • 50
    m
  • 150
    m
  • 50

    √

    18
    m
  • 75

    √

    2
    m
  • 50

    √

    3
    m