CBSE Board Practice

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CBSE Grade X - Some Applications of Trigonometry
Question 1
1.
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 45°. If the height of the flag staff is 11 m, find the height of the building .
  • 15.03 m
  • 10.03 m
  • 20.03 m
  • 18.03 m
  • 12.03 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 140 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 37°38' and 49°33' 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'
      37
      0.7536
      0.7563
      0.7590
      0.7618
      0.7646
      0.7673
      0.7701
      0.7729
      0.7757
      0.7785
      5
      9
      14
      19
      23
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      49
      1.1504
      1.1544
      1.1585
      1.1626
      1.1667
      1.1708
      1.1750
      1.1792
      1.1833
      1.1875
      7
      14
      21
      27
      34
  • 52.97 m
  • 47.97 m
  • 50.97 m
  • 42.97 m
  • 44.97 m
Question 3
3.
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 30° and 60° respectively. Find the height of the other temple.
  • 110.66 m
  • 128.66 m
  • 99.66 m
  • 106.66 m
  • 90.66 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 50°19'. If the height of the tower is 18 m, find the distance between the observation point and the top of the tower.
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      50
      1.1918
      1.1960
      1.2002
      1.2045
      1.2088
      1.2131
      1.2174
      1.2218
      1.2261
      1.2305
      7
      14
      22
      29
      36
    • From Table of Natural Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      50
      0.7660
      0.7672
      0.7683
      0.7694
      0.7705
      0.7716
      0.7727
      0.7738
      0.7749
      0.7760
      2
      4
      6
      7
      9
  • 26.39 m
  • 28.39 m
  • 23.39 m
  • 18.39 m
  • 20.39 m
Question 5
5.
If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?
  • ∠d
  • ∠e
  • ∠g
  • ∠f
Question 6
6.
    • 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
    • cosec
      (-1)
       
      (
      7
      6
      )
    • .
    • If the height of the
    • tower
    • is
    • 20 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • tower
    • .
  • 23.33 m
  • 28.33 m
  • 18.33 m
  • 26.33 m
  • 20.33 m
Question 7
7.
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 14 min for the angle of depression to change from 45° to 60°, how soon after this, will the car reach the observation tower?
  • 19 min 7 sec
  • 18 min 11 sec
  • 21 min 14 sec
  • 17 min 10 sec
  • 20 min 13 sec
Question 8
8.
The shadow of a vertical tower BA on a level ground is increased by 35 m, when the altitude of the sun changes from 45° to 30°. Find the height of the tower .
  • 52.82 m
  • 50.82 m
  • 42.82 m
  • 47.82 m
  • 44.82 m
Question 9
9.
    • 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 46°11' and 50°26' 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'
      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'
      50
      1.1918
      1.1960
      1.2002
      1.2045
      1.2088
      1.2131
      1.2174
      1.2218
      1.2261
      1.2305
      7
      14
      22
      29
      36
      • height =
      • 14.8 m
      • , distances away =
      • 11.88 m
      • ,
      • 14.12 m
      • height =
      • 16.8 m
      • , distances away =
      • 13.88 m
      • ,
      • 16.12 m
      • height =
      • 15.8 m
      • , distances away =
      • 12.88 m
      • ,
      • 15.12 m
      • height =
      • 17.8 m
      • , distances away =
      • 14.88 m
      • ,
      • 17.12 m
      • height =
      • 18.8 m
      • , distances away =
      • 15.88 m
      • ,
      • 18.12 m
Question 10
10.
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 45°. If the height of the tower is 80 m, find the height of the building .
  • 41.19 m
  • 46.19 m
  • 43.19 m
  • 51.19 m
  • 49.19 m