CBSE Board Practice

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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
    • sin
      (-1)
       
      (
      1
      7
      )
    • .
    • If the distance between the point and the top of the
    • tower
    • is
    • 190 m
    • ,
    • find the height of the
    • tower
    • .
  • 32.14 m
  • 22.14 m
  • 24.14 m
  • 30.14 m
  • 27.14 m
Question 2
2.
    • 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
    • 30°
    • .
    • If the height of the
    • tower
    • is
    • 90 m
    • ,
    • find the distance between
    • the observation point and the foot of the
    • tower
    • .
  • 90

    √

    18
    m
  • 135

    √

    2
    m
  • 90
    m
  • 90

    √

    3
    m
  • 270
    m
Question 3
3.
Two poles of equal height are standing opposite to each other on either side of a road which is 30 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30° and 45° respectively. Find the height of each pole and the distances of the point from the two poles .
      • height =
      • 9.98 m
      • , distances away =
      • 9.98 m
      • ,
      • 18.02 m
      • height =
      • 12.98 m
      • , distances away =
      • 12.98 m
      • ,
      • 21.02 m
      • height =
      • 11.98 m
      • , distances away =
      • 11.98 m
      • ,
      • 20.02 m
      • height =
      • 8.98 m
      • , distances away =
      • 8.98 m
      • ,
      • 17.02 m
      • height =
      • 10.98 m
      • , distances away =
      • 10.98 m
      • ,
      • 19.02 m
Question 4
4.
    • The angle of elevation of the top of a building from the foot of a tower is 44°39'. The angle of elevation of the top of the tower from the foot of the building is 22°11'. If the height of the tower is 95 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'
      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'
      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
  • 242.12 m
  • 204.12 m
  • 230.12 m
  • 254.12 m
  • 227.12 m
Question 5
5.
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 60° and 30° respectively. Find the height of the pillar.
  • 224.94 m
  • 256.94 m
  • 230.94 m
  • 205.94 m
  • 232.94 m
Question 6
6.
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 8 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?
  • 12 min 58 sec
  • 7 min 53 sec
  • 9 min 55 sec
  • 10 min 56 sec
  • 11 min 57 sec
Question 7
7.
    • 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
    • 150 m
    • ,
    • find the height of the
    • tower
    • .
  • 75
    2

    √

    12
    m
  • 150
    m
  • 75

    √

    2
    m
  • 75
    m
  • 150

    √

    3
    m
Question 8
8.
The shadow of a vertical tower BA on a level ground is increased by 40 m, when the altitude of the sun changes from 60° to 45°. Find the height of the tower .
  • 89.64 m
  • 91.64 m
  • 99.64 m
  • 97.64 m
  • 94.64 m
Question 9
9.
From a point 120 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 cliff.
  • 72.29 m
  • 64.29 m
  • 74.29 m
  • 66.29 m
  • 69.29 m
Question 10
10.
    • 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
    • 45°
    • .
    • If the distance between the point and the foot of the
    • building
    • is
    • 60 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • building
    • .
  • 60

    √

    2
    m
  • 30

    √

    12
    m
  • 120

    √

    3
    m
  • 60
    m
  • 120
    m