CBSE Board Practice

Class VI Class VII Class VIII Class IX Class X
CBSE Grade X - Some Applications of Trigonometry
Question 1
1.
    • 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)
       
      (
      1
      5
      )
    • .
    • If the height of the
    • tower
    • is
    • 110 m
    • ,
    • find the distance between
    • the observation point and the foot of the
    • tower
    • .
  • 27.00 m
  • 25.00 m
  • 19.00 m
  • 17.00 m
  • 22.00 m
Question 2
2.
    • 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 59°54'. If the distance between the observation point and the foot of the chimney is 10 m, find the height of the chimney.
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      59
      1.6643
      1.6709
      1.6775
      1.6842
      1.6909
      1.6977
      1.7045
      1.7113
      1.7182
      1.7251
      11
      23
      34
      45
      56
    • From Table of Natural Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      59
      0.5151
      0.5135
      0.5120
      0.5105
      0.5090
      0.5075
      0.5080
      0.5045
      0.5030
      0.5015
      3
      5
      8
      10
      13
  • 22.25 m
  • 20.25 m
  • 17.25 m
  • 12.25 m
  • 14.25 m
Question 3
3.
    • 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 47°50' and the angle of elevation of the top of the building is 45°6'. If the height of the flag staff is 12 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'
      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
    • 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
  • 119.70 m
  • 144.70 m
  • 113.70 m
  • 132.70 m
  • 97.70 m
Question 4
4.
    • The upper part of a tree is broken into two parts without being detatched. It makes an angle of 42°16' with the ground. The top of the tree touches the ground at a distance of 150 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'
      42
      0.9004
      0.9036
      0.9067
      0.9099
      0.9131
      0.9163
      0.9195
      0.9228
      0.9260
      0.9293
      5
      11
      16
      21
      27
    • From Table of Natural Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      42
      0.7431
      0.7420
      0.7408
      0.7396
      0.7385
      0.7373
      0.7361
      0.7349
      0.7337
      0.7325
      2
      4
      6
      8
      10
  • 339.02 m
  • 331.02 m
  • 352.02 m
  • 324.02 m
  • 343.02 m
Question 5
5.
    • 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 height of the
    • chimney
    • is
    • 30 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • chimney
    • .
  • 20
    m
  • 20

    √

    3
    m
  • 20

    √

    18
    m
  • 60
    m
  • 30

    √

    2
    m
Question 6
6.
From a point 70 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 pillar.
  • 48.25 m
  • 46.25 m
  • 51.25 m
  • 56.25 m
  • 54.25 m
Question 7
7.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 90 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 60° respectively. Find the height of the other temple.
  • 55.00 m
  • 65.00 m
  • 57.00 m
  • 60.00 m
  • 63.00 m
Question 8
8.
The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the height of the tower is 70 m, find the height of the building .
  • 18.33 m
  • 23.33 m
  • 20.33 m
  • 28.33 m
  • 26.33 m
Question 9
9.
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 45° respectively. Find the height of the cliff.
  • 180.00 m
  • 167.00 m
  • 176.00 m
  • 182.00 m
  • 196.00 m
Question 10
10.
    • 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
    • cos
      (-1)
       
      (
      1
      2
      )
    • .
    • If the distance between the point and the foot of the
    • tower
    • is
    • 10 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • tower
    • .
  • 25.00 m
  • 17.00 m
  • 20.00 m
  • 23.00 m
  • 15.00 m