CBSE Board Practice

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CBSE Grade X - Some Applications of Trigonometry
Question 1
1.
From a point 180 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.
  • 207.85 m
  • 183.85 m
  • 224.85 m
  • 191.85 m
  • 215.85 m
Question 2
2.
A man in a boat rowing away from a lighthouse 65 m high, takes 3 min to change the angle of elevation of the top of the lighthouse from 45° to 30°. Find the speed of the boat.
  • 1.26 m/sec
  • 7.26 m/sec
  • 0.26 m/sec
  • 8.26 m/sec
  • 2.26 m/sec
Question 3
3.
    • From the top of a 17 m high building , the angle of elevation of the top of a cable tower is 44°54' and the angle of depression of its foot is 36°5'. Find the height of the cable tower.
    • 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
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      36
      0.7265
      0.7292
      0.7319
      0.7346
      0.7373
      0.7400
      0.7427
      0.7454
      0.7481
      0.7508
      5
      9
      14
      18
      23
  • 40.24 m
  • 37.24 m
  • 45.24 m
  • 43.24 m
  • 35.24 m
Question 4
4.
A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards him. If it takes 19 min for the angle of depression to change from 45° to 60°, how soon after this, will the car reach the observation tower?
  • 24 min 56 sec
  • 23 min 54 sec
  • 27 min 60 sec
  • 26 min 58 sec
  • 25 min 57 sec
Question 5
5.
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 45° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 16 m, find the height of the building .
  • 18.86 m
  • 26.86 m
  • 16.86 m
  • 21.86 m
  • 24.86 m
Question 6
6.
From a point 80 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 45° respectively. Find the height of the cliff.
  • 75.00 m
  • 77.00 m
  • 85.00 m
  • 80.00 m
  • 83.00 m
Question 7
7.
    • 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
    • 60°
    • .
    • If the distance between the point and the top of the
    • chimney
    • is
    • 150 m
    • ,
    • find the height of the
    • chimney
    • .
  • 225
    2

    √

    2
    m
  • 75
    m
  • 75

    √

    3
    m
  • 225
    m
  • 75

    √

    18
    m
Question 8
8.
    • 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 34°41'. If the height of the building is 11 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'
      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
  • 10.89 m
  • 20.89 m
  • 12.89 m
  • 15.89 m
  • 18.89 m
Question 9
9.
    • The upper part of a tree is broken into two parts without being detatched. It makes an angle of 33°24' with the ground. The top of the tree touches the ground at a distance of 190 m from the foot of the tree . Find the height of the tree before it was broken.
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      33
      0.6494
      0.6519
      0.6544
      0.6569
      0.6594
      0.6619
      0.6644
      0.6669
      0.6694
      0.6720
      4
      8
      13
      17
      21
    • From Table of Natural Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      33
      0.8387
      0.8377
      0.8368
      0.8358
      0.8348
      0.8339
      0.8329
      0.8320
      0.8310
      0.8300
      2
      3
      5
      7
      8
  • 370.89 m
  • 345.89 m
  • 336.89 m
  • 368.89 m
  • 352.89 m
Question 10
10.
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 45° and 60° and the distance between them is 125 m , find the height of the cliff.
  • 82.25 m
  • 84.25 m
  • 79.25 m
  • 76.25 m
  • 74.25 m