ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Heights and Distances
Question 1
1.
    • 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 60°35'. If the height of the radio tower is 9 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'
      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
    • From Table of Natural Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      60
      0.8660
      0.8669
      0.8678
      0.8686
      0.8695
      0.8704
      0.8712
      0.8721
      0.8729
      0.8738
      1
      3
      4
      6
      7
  • 5.33 m
  • 13.33 m
  • 10.33 m
  • 15.33 m
  • 7.33 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 43°23'. If the height of the building is 12 m, find the distance between the observation point and the foot of the building.
    • 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
    • From Table of Natural Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      43
      0.6820
      0.6833
      0.6845
      0.6858
      0.6871
      0.6884
      0.6896
      0.6909
      0.6921
      0.6934
      2
      4
      6
      9
      11
  • 17.70 m
  • 12.70 m
  • 7.70 m
  • 15.70 m
  • 9.70 m
Question 3
3.
    • A
    • tower
    • stands vertically on the ground.
    • The height of the
    • tower
    • is
    • 200

      √

      3
      m
    • .
    • The distance between the observation point and its foot
    • is
    • 600
      m
    • .
    • Find the angle of elevation.
  • 90°
  • 45°
  • 30°
  • 75°
  • 60°
Question 4
4.
A man in a boat rowing away from a lighthouse 50 m high, takes 1.5 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.
  • 1.23 m/sec
  • 2.23 m/sec
  • 7.23 m/sec
  • 8.23 m/sec
  • 0.23 m/sec
Question 5
5.
    • 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 23° and 47° and the distance between them is 180 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'
      23
      0.4245
      0.4265
      0.4286
      0.4307
      0.4327
      0.4348
      0.4369
      0.4390
      0.4411
      0.4431
      3
      7
      10
      14
      17
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      47
      1.0724
      1.0761
      1.0799
      1.0837
      1.0875
      1.0913
      1.0951
      1.0990
      1.1028
      1.1067
      6
      13
      19
      25
      32
  • 59.74 m
  • 49.74 m
  • 57.74 m
  • 54.74 m
  • 51.74 m
Question 6
6.
An observer 1.4 m tall, is 170 m away from a tower . The angle of elevation of the top of the tower from her eyes is 45°. Find the height of the tower .
  • 171.40 m
  • 184.40 m
  • 197.40 m
  • 163.40 m
  • 144.40 m
Question 7
7.
    • Two poles of equal height are standing opposite to each other on either side of a road which is 15 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 20°42' and 44°11' respectively. Find the height of each pole and the distances of the point from the two poles .
    • 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
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      44
      0.9657
      0.9691
      0.9725
      0.9759
      0.9793
      0.9827
      0.9861
      0.9896
      0.9930
      0.9965
      6
      11
      17
      23
      28
      • height =
      • 3.08 m
      • , distances away =
      • 3.2 m
      • ,
      • 9.8 m
      • height =
      • 5.08 m
      • , distances away =
      • 5.2 m
      • ,
      • 11.8 m
      • height =
      • 4.08 m
      • , distances away =
      • 4.2 m
      • ,
      • 10.8 m
      • height =
      • 2.08 m
      • , distances away =
      • 2.2 m
      • ,
      • 8.8 m
      • height =
      • 6.08 m
      • , distances away =
      • 6.2 m
      • ,
      • 12.8 m
Question 8
8.
    • 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 48°6' and the angle of elevation of the top of the building is 34°58'. If the height of the building is 16 m, find the height of the flag staff .
    • 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 Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      48
      1.1106
      1.1145
      1.1184
      1.1224
      1.1263
      1.1303
      1.1343
      1.1383
      1.1423
      1.1463
      7
      13
      20
      27
      33
  • 8.50 m
  • 10.50 m
  • 9.50 m
  • 11.50 m
  • 7.50 m
Question 9
9.
If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?
  • ∠f
  • ∠e
  • ∠d
  • ∠g
Question 10
10.
    • Two vertical poles are on either side of a road. A 21 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 36°45' with the pole and when it is turned to rest against another pole, it makes an angle of 22°11' with the road. Find the width of the road.
    • From Table of Natural Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      36
      0.8090
      0.8080
      0.8070
      0.8059
      0.8049
      0.8039
      0.8028
      0.8018
      0.8007
      0.7997
      2
      3
      5
      7
      8
    • From Table of Natural Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      22
      0.9272
      0.9263
      0.9259
      0.9252
      0.9245
      0.9239
      0.9232
      0.9225
      0.9219
      0.9212
      1
      2
      3
      5
      6
  • 33.27 m
  • 39.27 m
  • 41.27 m
  • 36.27 m
  • 31.27 m