CBSE Board Practice

Class VI Class VII Class VIII Class IX Class X
CBSE Grade X - Some Applications of Trigonometry
Question 1
1.
From the top of a 8 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Find the height of the cable tower.
  • 27.00 m
  • 29.00 m
  • 32.00 m
  • 37.00 m
  • 35.00 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 160 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°4' and 52°15' respectively. Find the height of the other temple.
    • 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'
      52
      1.2799
      1.2846
      1.2892
      1.2938
      1.2985
      1.3032
      1.3079
      1.3127
      1.3175
      1.3222
      8
      16
      24
      31
      39
  • 87.38 m
  • 85.38 m
  • 82.38 m
  • 77.38 m
  • 79.38 m
Question 3
3.
    • 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 36°44'. If the distance between the observation point and the foot of the building is 14 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'
      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
    • 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
  • 10.45 m
  • 15.45 m
  • 5.45 m
  • 13.45 m
  • 7.45 m
Question 4
4.
    • From the top of a 18 m high building , the angle of elevation of the top of a cable tower is 46°18' and the angle of depression of its foot is 45°1'. 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'
      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'
      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
  • 41.82 m
  • 33.82 m
  • 39.82 m
  • 31.82 m
  • 36.82 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
    • 45°
    • .
    • If the distance between the point and the top of the
    • tower
    • is
    • 60 m
    • ,
    • find the height of the
    • tower
    • .
  • 60

    √

    3
    m
  • 15

    √

    12
    m
  • 60
    m
  • 30
    m
  • 30

    √

    2
    m
Question 6
6.
From a point 200 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.
  • 87.52 m
  • 81.52 m
  • 84.52 m
  • 79.52 m
  • 89.52 m
Question 7
7.
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
    m
  • 10
    3
    m
  • 5

    √

    2
    m
  • 10
    3

    √

    3
    m
Question 8
8.
    • 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 33°6'. If the height of the tower is 6 m, find the distance between the observation point and the foot of the tower.
    • 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 Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      33
      0.5446
      0.5461
      0.5476
      0.5490
      0.5505
      0.5519
      0.5534
      0.5548
      0.5563
      0.5577
      2
      5
      7
      10
      12
  • 9.20 m
  • 10.20 m
  • 8.20 m
  • 11.20 m
  • 7.20 m
Question 9
9.
Two boys are on opposite sides of a tower of 120 m height. They measure the angle of elevation of the top of the tower as 45° and 60° respectively. Find the distance between the two boys.
  • (
    60

    √

    6
    +
    60

    √

    2
    )
    m
  • (
    120

    √

    6
    +
    40

    √

    18
    )
    m
  • 9600
    m
  • (
    120
    +
    40

    √

    3
    )
    m
  • (
    2
    +

    √

    3
    )
    m
Question 10
10.
Two poles of equal height are standing opposite to each other on either side of a road which is 10 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 45° and 30° respectively. Find the height of each pole and the distances of the point from the two poles .
      • height =
      • 3.66 m
      • , distances away =
      • 6.34 m
      • ,
      • 3.66 m
      • height =
      • 5.66 m
      • , distances away =
      • 8.34 m
      • ,
      • 5.66 m
      • height =
      • 2.66 m
      • , distances away =
      • 5.34 m
      • ,
      • 2.66 m
      • height =
      • 1.66 m
      • , distances away =
      • 4.34 m
      • ,
      • 1.66 m
      • height =
      • 4.66 m
      • , distances away =
      • 7.34 m
      • ,
      • 4.66 m