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 19 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 30°. Find the height of the cable tower.
  • 79.00 m
  • 81.00 m
  • 76.00 m
  • 71.00 m
  • 73.00 m
Question 2
2.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 200 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 height of the other temple.
  • 116.33 m
  • 128.33 m
  • 151.33 m
  • 150.33 m
  • 133.33 m
Question 3
3.
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 30° and 60° and the distance between them is 225 m , find the height of the cliff.
  • 92.43 m
  • 97.43 m
  • 100.43 m
  • 102.43 m
  • 94.43 m
Question 4
4.
    • From a point 150 m above a lake, the angle of elevation of a cloud is 27° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud from the lake.
    • 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
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      60
      1.7321
      1.7391
      1.7461
      1.7532
      1.7603
      1.7675
      1.7747
      1.7820
      1.7893
      1.7966
      12
      24
      36
      48
      60
  • 292.02 m
  • 248.02 m
  • 275.02 m
  • 279.02 m
  • 269.02 m
Question 5
5.
A person, walking 45 m from a point toward a flagpost , observes that its angle of elevation changes from 45° to 60°. Find the height of the flagpost .
  • (
    135
    2

    √

    6
    +
    45
    2

    √

    18
    )
    m
  • (
    135
    4

    √

    6
    +
    135
    4

    √

    2
    )
    m
  • 6075
    2
    m
  • (
    135
    2
    +
    45
    2

    √

    3
    )
    m
  • (
    2
    +

    √

    3
    )
    m
Question 6
6.
A man in a boat rowing away from a lighthouse 85 m high, takes 3.5 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.
  • 0.17 m/sec
  • 2.17 m/sec
  • 7.17 m/sec
  • 8.17 m/sec
  • 1.17 m/sec
Question 7
7.
The angles of depression of two boats from the top of a cliff 80 m high are 45° and 60° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
  • 109.19 m
  • 122.19 m
  • 132.19 m
  • 126.19 m
  • 148.19 m
Question 8
8.
    • 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
    • sin
      (-1)
       
      (
      3
      8
      )
    • .
    • If the distance between the point and the top of the
    • tower
    • is
    • 140 m
    • ,
    • find the height of the
    • tower
    • .
  • 52.50 m
  • 49.50 m
  • 57.50 m
  • 47.50 m
  • 55.50 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
    • cosec
      (-1)
       
      (
      8
      5
      )
    • .
    • If the distance between the point and the top of the
    • tower
    • is
    • 140 m
    • ,
    • find the height of the
    • tower
    • .
  • 90.50 m
  • 84.50 m
  • 82.50 m
  • 92.50 m
  • 87.50 m
Question 10
10.
    • 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
    • 30°
    • .
    • If the distance between the point and the top of the
    • chimney
    • is
    • 70 m
    • ,
    • find the height of the
    • chimney
    • .
  • 35
    m
  • 32
    m
  • 37
    m
  • 34
    m
  • 36
    m