CBSE Board Practice

Class VI Class VII Class VIII Class IX Class X
CBSE Grade X - Some Applications of Trigonometry
Question 1
1.
The angles of depression of two boats from the top of a cliff 150 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
  • 422.82 m
  • 407.82 m
  • 416.82 m
  • 394.82 m
  • 409.82 m
Question 2
2.
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 building is 15 m, find the height of the flag staff .
  • 10.98 m
  • 15.98 m
  • 5.98 m
  • 13.98 m
  • 7.98 m
Question 3
3.
    • 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)
       
      (
      3
      4
      )
    • .
    • If the distance between the point and the top of the
    • tower
    • is
    • 60 m
    • ,
    • find the height of the
    • tower
    • .
  • 48.00 m
  • 40.00 m
  • 50.00 m
  • 45.00 m
  • 42.00 m
Question 4
4.
The angles of depression of two boats from the top of a cliff 110 m high are 45° and 30° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
  • 80.53 m
  • 83.53 m
  • 85.53 m
  • 75.53 m
  • 77.53 m
Question 5
5.
Two vertical poles are on either side of a road. A 29 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 45° with the pole and when it is turned to rest against another pole, it makes an angle of 30° with the road. Find the width of the road.
  • 45.62 m
  • 42.62 m
  • 40.62 m
  • 48.62 m
  • 50.62 m
Question 6
6.
    • The upper part of a tree is broken into two parts without being detatched. It makes an angle of 47°5' with the ground. The top of the tree touches the ground at a distance of 140 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'
      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
    • From Table of Natural Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      47
      0.6820
      0.6807
      0.6794
      0.6784
      0.6769
      0.6756
      0.6743
      0.6730
      0.6717
      0.6704
      2
      4
      6
      9
      11
  • 343.19 m
  • 356.19 m
  • 360.19 m
  • 350.19 m
  • 373.19 m
Question 7
7.
    • An observer 1.4 m tall, is 70 m away from a tower . The angle of elevation of the top of the tower from her eyes is 57°11'. Find the height of the tower .
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      57
      1.5399
      1.5458
      1.5517
      1.5577
      1.5637
      1.5697
      1.5757
      1.5818
      1.5880
      1.5941
      10
      20
      30
      40
      50
  • 109.96 m
  • 82.96 m
  • 97.96 m
  • 124.96 m
  • 113.96 m
Question 8
8.
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 6 min for the angle of depression to change from 30° to 60°, how soon after this, will the car reach the observation tower?
  • 2 min 4 sec
  • 6 min 7 sec
  • 3 min 0 sec
  • 0 min 3 sec
  • 4 min 6 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 58°49'. If the height of the radio tower is 4 m, find the distance between the observation point and the top 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'
      58
      1.6003
      1.6066
      1.6128
      1.6191
      1.6255
      1.6319
      1.6383
      1.6447
      1.6512
      1.6577
      11
      21
      32
      43
      53
    • From Table of Natural Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      58
      0.8450
      0.8490
      0.8499
      0.8508
      0.8517
      0.8526
      0.8536
      0.8545
      0.8554
      0.8563
      2
      3
      5
      6
      8
  • 4.68 m
  • 5.68 m
  • 3.68 m
  • 6.68 m
  • 2.68 m
Question 10
10.
Two poles of equal height are standing opposite to each other on either side of a road which is 20 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 45° and 60° respectively. Find the height of each pole and the distances of the point from the two poles .
      • height =
      • 13.68 m
      • , distances away =
      • 8.32 m
      • ,
      • 13.68 m
      • height =
      • 14.68 m
      • , distances away =
      • 9.32 m
      • ,
      • 14.68 m
      • height =
      • 11.68 m
      • , distances away =
      • 6.32 m
      • ,
      • 11.68 m
      • height =
      • 12.68 m
      • , distances away =
      • 7.32 m
      • ,
      • 12.68 m
      • height =
      • 10.68 m
      • , distances away =
      • 5.32 m
      • ,
      • 10.68 m