CBSE Board Practice

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CBSE Grade X - Some Applications of Trigonometry
Question 1
1.
    • 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 24°35' and 22°28' 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'
      24
      0.4452
      0.4473
      0.4494
      0.4515
      0.4536
      0.4557
      0.4578
      0.4599
      0.4621
      0.4642
      4
      7
      11
      14
      18
    • 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
      • height =
      • 2.34 m
      • , distances away =
      • 8.51 m
      • ,
      • 7.49 m
      • height =
      • 6.34 m
      • , distances away =
      • 12.51 m
      • ,
      • 11.49 m
      • height =
      • 4.34 m
      • , distances away =
      • 10.51 m
      • ,
      • 9.49 m
      • height =
      • 5.34 m
      • , distances away =
      • 11.51 m
      • ,
      • 10.49 m
      • height =
      • 3.34 m
      • , distances away =
      • 9.51 m
      • ,
      • 8.49 m
Question 2
2.
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 3
3.
A man 1.9 m tall stands at a distance of 3.3 m from a lamp post and casts a shadow of 7.1 m on the ground. Find the height of the lamp post .
  • 1.78 m
  • 2.78 m
  • 3.78 m
  • 0.78 m
  • 4.78 m
Question 4
4.
    • 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 27°41' and the angle of elevation of the top of the building is 23°42'. If the height of the flag staff 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'
      23
      0.4245
      0.4265
      0.4286
      0.4307
      0.4327
      0.4348
      0.4369
      0.4390
      0.4411
      0.4431
      3
      7
      10
      14
      17
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      27
      0.5095
      0.5117
      0.5139
      0.5161
      0.5184
      0.5206
      0.5228
      0.5250
      0.5272
      0.5295
      4
      7
      11
      15
      18
  • 74.80 m
  • 68.80 m
  • 71.80 m
  • 66.80 m
  • 76.80 m
Question 5
5.
    • There are two temples one on each bank of a river, just opposite to each other. One of the temples is 40 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 42°39' and 51°10' respectively. Find the width of the river .
    • 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 Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      51
      1.2349
      1.2393
      1.2437
      1.2484
      1.2527
      1.2572
      1.2617
      1.2662
      1.2708
      1.2753
      8
      15
      23
      30
      38
  • 35.20 m
  • 27.20 m
  • 37.20 m
  • 29.20 m
  • 32.20 m
Question 6
6.
The angles of depression of two boats from the top of a cliff 50 m high are 30° and 60° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
  • 115.48 m
  • 107.48 m
  • 91.48 m
  • 127.48 m
  • 120.48 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 190 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 width of the river .
  • 92.69 m
  • 127.69 m
  • 123.69 m
  • 109.69 m
  • 106.69 m
Question 8
8.
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.
  • 130.66 m
  • 106.66 m
  • 124.66 m
  • 90.66 m
  • 81.66 m
Question 9
9.
A person, walking 5 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 60°. Find the height of the flagpost .
  • 15
    2
    m
  • 5
    2
    m
  • 5
    2

    √

    18
    m
  • 5
    2

    √

    3
    m
  • 15
    4

    √

    2
    m
Question 10
10.
    • An aeroplane is flying horizontally 700 m above the ground. From a point of observation, which lies exactly below the path of the aeroplane, the angle of elevation at a certain instant is 66°. After 10 sec , its elevation from the same point changes to 40°. Find the uniform speed of the aeroplane .
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      40
      0.8391
      0.8421
      0.8451
      0.8481
      0.8511
      0.8541
      0.8571
      0.8601
      0.8632
      0.8662
      5
      10
      15
      20
      25
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      66
      2.2460
      2.2566
      2.2673
      2.2781
      2.2889
      2.2998
      2.3109
      2.3220
      2.3332
      2.3445
      18
      37
      55
      73
      92
  • 188.12 kmph
  • 172.12 kmph
  • 206.12 kmph
  • 173.12 kmph