ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Heights and Distances
Question 1
1.
If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?
  • ∠c
  • ∠e
  • ∠d
  • ∠f
Question 2
2.
    • An observer 1.7 m tall, is 200 m away from a tower . The angle of elevation of the top of the tower from her eyes is 37°20'. Find the height of the tower .
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      37
      0.7536
      0.7563
      0.7590
      0.7618
      0.7646
      0.7673
      0.7701
      0.7729
      0.7757
      0.7785
      5
      9
      14
      19
      23
  • 127.24 m
  • 171.24 m
  • 162.24 m
  • 138.24 m
  • 154.24 m
Question 3
3.
    • The angle of elevation of the top of a building from the foot of a tower is 22°25'. The angle of elevation of the top of the tower from the foot of the building is 40°16'. If the height of the tower is 80 m, find the height of the building .
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      22
      0.4040
      0.4061
      0.4081
      0.4101
      0.4122
      0.4142
      0.4163
      0.4183
      0.4202
      0.4224
      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'
      40
      0.8391
      0.8421
      0.8451
      0.8481
      0.8511
      0.8541
      0.8571
      0.8601
      0.8632
      0.8662
      5
      10
      15
      20
      25
  • 38.96 m
  • 43.96 m
  • 35.96 m
  • 41.96 m
  • 33.96 m
Question 4
4.
From the top of a light house which is 65 m high from the sea level, the angles of depression of two ships are 60° and 30°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
  • 72.05 m
  • 75.05 m
  • 70.05 m
  • 80.05 m
  • 78.05 m
Question 5
5.
From a point 150 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 30° respectively. Find the height of the pillar.
  • 191.20 m
  • 187.20 m
  • 170.20 m
  • 156.20 m
  • 173.20 m
Question 6
6.
    • 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 46° and 20° and the distance between them is 205 m , 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'
      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
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      20
      0.3640
      0.3659
      0.3679
      0.3699
      0.3719
      0.3739
      0.3759
      0.3779
      0.3799
      0.3819
      3
      7
      10
      13
      17
  • 52.21 m
  • 58.21 m
  • 55.21 m
  • 50.21 m
  • 60.21 m
Question 7
7.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60° with the ground. The top of the tree touches the ground at a distance of 80 m from the foot of the tree . Find the height of the tree before it was broken.
  • 294.57 m
  • 325.57 m
  • 304.57 m
  • 276.57 m
  • 298.57 m
Question 8
8.
    • 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 34°32'. If the height of the pole is 3 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'
      34
      0.6745
      0.6771
      0.6796
      0.6822
      0.6847
      0.6873
      0.6899
      0.6924
      0.6930
      0.6976
      4
      9
      13
      17
      22
    • From Table of Natural Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      34
      0.5592
      0.5606
      0.5621
      0.5635
      0.5650
      0.5664
      0.5678
      0.5693
      0.5707
      0.5721
      2
      5
      7
      9
      12
  • 6.29 m
  • 5.29 m
  • 4.29 m
  • 3.29 m
  • 7.29 m
Question 9
9.
A flagstaff stands on the top of a building at a distance of 5 m away from the foot of building . The angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 30°. Find the height of the flagstaff .
  • 10
    3

    √

    18
    m
  • 10
    3
    m
  • 10
    m
  • 5

    √

    2
    m
  • 10
    3

    √

    3
    m
Question 10
10.
    • From a point 70 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 45°39' and 37°23' 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'
      37
      0.7536
      0.7563
      0.7590
      0.7618
      0.7646
      0.7673
      0.7701
      0.7729
      0.7757
      0.7785
      5
      9
      14
      19
      23
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      45
      1.0000
      1.0035
      1.0070
      1.0105
      1.0141
      1.0176
      1.0212
      1.0247
      1.0283
      1.0319
      6
      12
      18
      24
      30
  • 50.49 m
  • 56.49 m
  • 53.49 m
  • 58.49 m
  • 48.49 m