ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Heights and Distances
Question 1
1.
A person, walking 45 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 60°. Find the height of the flagpost .
  • 45
    2

    √

    3
    m
  • 45
    2
    m
  • 135
    2
    m
  • 135
    4

    √

    2
    m
  • 45
    2

    √

    18
    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 32°52' and 38°15' 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'
      32
      0.6249
      0.6273
      0.6297
      0.6322
      0.6346
      0.6371
      0.6395
      0.6420
      0.6445
      0.6469
      4
      8
      12
      17
      21
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      38
      0.7813
      0.7841
      0.7869
      0.7898
      0.7926
      0.7954
      0.7983
      0.8012
      0.8040
      0.8069
      5
      9
      14
      19
      23
  • 237.71 m
  • 241.71 m
  • 253.71 m
  • 271.71 m
  • 266.71 m
Question 3
3.
    • An aeroplane is flying horizontally 1000 m above the ground. From a point of observation, which lies exactly below the path of the aeroplane, the angle of elevation at a certain instant is 50°. After 10 sec , its elevation from the same point changes to 22°. Find the uniform speed of the aeroplane .
    • 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'
      50
      1.1918
      1.1960
      1.2002
      1.2045
      1.2088
      1.2131
      1.2174
      1.2218
      1.2261
      1.2305
      7
      14
      22
      29
      36
  • 572.02 kmph
  • 589.02 kmph
  • 577.02 kmph
  • 592.02 kmph
  • 614.02 kmph
Question 4
4.
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 30° and 45° respectively. Find the height of the other temple.
  • 21.13 m
  • 26.13 m
  • 24.13 m
  • 16.13 m
  • 18.13 m
Question 5
5.
    • An observer 1.8 m tall, is 40 m away from a tower . The angle of elevation of the top of the tower from her eyes is 55°52'. 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'
      55
      1.4281
      1.4335
      1.4388
      1.4442
      1.4496
      1.4550
      1.4605
      1.4659
      1.4715
      1.4770
      9
      18
      27
      36
      45
  • 55.80 m
  • 63.80 m
  • 60.80 m
  • 57.80 m
  • 65.80 m
Question 6
6.
    • 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 57°23'. If the distance between the observation point and the top of the tower is 12 m, find the distance between the observation point and the foot of the tower.
    • From Table of Natural Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      57
      0.8387
      0.8396
      0.8406
      0.8415
      0.8425
      0.8434
      0.8443
      0.8453
      0.8462
      0.8471
      2
      3
      5
      6
      8
    • From Table of Natural Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      57
      0.5446
      0.5432
      0.5417
      0.5402
      0.5388
      0.5373
      0.5358
      0.5344
      0.5329
      0.5314
      2
      5
      7
      10
      12
  • 5.47 m
  • 7.47 m
  • 6.47 m
  • 4.47 m
  • 8.47 m
Question 7
7.
The angles of depression of two boats from the top of a cliff 190 m high are 45° and 60° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
  • 75.29 m
  • 83.29 m
  • 85.29 m
  • 77.29 m
  • 80.29 m
Question 8
8.
A man in a boat rowing away from a lighthouse 75 m high, takes 3.5 min to change the angle of elevation of the top of the lighthouse from 45° to 30°. Find the speed of the boat.
  • 2.26 m/sec
  • 0.26 m/sec
  • 1.26 m/sec
  • 7.26 m/sec
  • 8.26 m/sec
Question 9
9.
From a point 60 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° and 30° respectively. Find the height of the pillar.
  • 20.36 m
  • 28.36 m
  • 22.36 m
  • 25.36 m
  • 30.36 m
Question 10
10.
Two vertical poles are on either side of a road. A 20 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 60° with the pole and when it is turned to rest against another pole, it makes an angle of 30° with the road. Find the width of the road.
  • 27.32 m
  • 22.32 m
  • 32.32 m
  • 30.32 m
  • 24.32 m