CBSE Board Practice

Class VI Class VII Class VIII Class IX Class X
CBSE Grade X - Some Applications of Trigonometry
Question 1
1.
    • 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 56°29'. If the distance between the observation point and the top of the pole is 19 m, find the height of the pole.
    • From Table of Natural Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      56
      0.8290
      0.8300
      0.8310
      0.8320
      0.8329
      0.8339
      0.8348
      0.8358
      0.8369
      0.8377
      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'
      56
      0.5592
      0.5577
      0.5563
      0.5548
      0.5534
      0.5519
      0.5505
      0.5490
      0.5476
      0.5461
      2
      5
      7
      10
      12
  • 10.84 m
  • 12.84 m
  • 20.84 m
  • 18.84 m
  • 15.84 m
Question 2
2.
From the top of a light house which is 65 m high from the sea level, the angles of depression of two ships are 45° 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.
  • 47.57 m
  • 50.57 m
  • 44.57 m
  • 52.57 m
  • 42.57 m
Question 3
3.
    • Two poles of equal height are standing opposite to each other on either side of a road which is 45 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 23°39' and 46°45' 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'
      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'
      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
      • height =
      • 11.96 m
      • , distances away =
      • 11.13 m
      • ,
      • 29.87 m
      • height =
      • 15.96 m
      • , distances away =
      • 15.13 m
      • ,
      • 33.87 m
      • height =
      • 14.96 m
      • , distances away =
      • 14.13 m
      • ,
      • 32.87 m
      • height =
      • 13.96 m
      • , distances away =
      • 13.13 m
      • ,
      • 31.87 m
      • height =
      • 12.96 m
      • , distances away =
      • 12.13 m
      • ,
      • 30.87 m
Question 4
4.
    • 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
    • cot
      (-1)
       
      (
      4
      7
      )
    • .
    • If the distance between the point and the foot of the
    • tower
    • is
    • 170 m
    • ,
    • find the height of the
    • tower
    • .
  • 297.50 m
  • 311.50 m
  • 283.50 m
  • 280.50 m
  • 312.50 m
Question 5
5.
    • 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)
       
      (
      1
      3
      )
    • .
    • If the distance between the point and the top of the
    • tower
    • is
    • 150 m
    • ,
    • find the height of the
    • tower
    • .
  • 53.00 m
  • 55.00 m
  • 45.00 m
  • 50.00 m
  • 47.00 m
Question 6
6.
    • 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
    • 45°
    • .
    • If the height of the
    • radio tower
    • is
    • 50 m
    • ,
    • find the distance between
    • the observation point and the foot of the
    • radio tower
    • .
  • 49
    m
  • 51
    m
  • 47
    m
  • 52
    m
  • 50
    m
Question 7
7.
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 60° and the angle of elevation of the top of the building is 30°. If the height of the building is 17 m, find the height of the flag staff .
  • 37.00 m
  • 31.00 m
  • 39.00 m
  • 29.00 m
  • 34.00 m
Question 8
8.
A man in a boat rowing away from a lighthouse 25 m high, takes 3 min to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat.
  • 7.16 m/sec
  • 1.16 m/sec
  • 2.16 m/sec
  • 8.16 m/sec
  • 0.16 m/sec
Question 9
9.
    • 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 39°20'. If the height of the radio tower is 3 m, find the distance between the observation point and the foot 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'
      39
      0.8098
      0.8127
      0.8156
      0.8185
      0.8214
      0.8243
      0.8273
      0.8302
      0.8332
      0.8361
      5
      10
      15
      19
      24
    • From Table of Natural Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      39
      0.6293
      0.6307
      0.6320
      0.6334
      0.6347
      0.6361
      0.6374
      0.6388
      0.6401
      0.6414
      2
      5
      7
      9
      12
  • 3.66 m
  • 1.66 m
  • 2.66 m
  • 5.66 m
  • 4.66 m
Question 10
10.
A person, walking 10 m from a point toward a flagpost , observes that its angle of elevation changes from 45° to 60°. Find the height of the flagpost .
  • 150
    m
  • (
    2
    +

    √

    3
    )
    m
  • (
    15

    √

    6
    +
    5

    √

    18
    )
    m
  • (
    15
    +
    5

    √

    3
    )
    m
  • (
    15
    2

    √

    6
    +
    15
    2

    √

    2
    )
    m