CBSE Board Practice

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CBSE Grade X - Some Applications of Trigonometry
Question 1
1.
    • 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
    • 60°
    • .
    • If the distance between the point and the top of the
    • radio tower
    • is
    • 180 m
    • ,
    • find the height of the
    • radio tower
    • .
  • 90

    √

    3
    m
  • 90

    √

    18
    m
  • 90
    m
  • 270
    m
  • 135

    √

    2
    m
Question 2
2.
A man in a boat rowing away from a lighthouse 90 m high, takes 0.5 min to change the angle of elevation of the top of the lighthouse from 45° to 30°. Find the speed of the boat.
  • 4.20 m/sec
  • 2.20 m/sec
  • 1.20 m/sec
  • 0.20 m/sec
  • 3.20 m/sec
Question 3
3.
The angle of elevation of the top of a building from the foot of a tower is 60°. The angle of elevation of the top of the tower from the foot of the building is 30°. If the height of the tower is 45 m, find the height of the building .
  • 148.99 m
  • 111.99 m
  • 152.99 m
  • 134.99 m
  • 131.99 m
Question 4
4.
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 10 min for the angle of depression to change from 45° to 60°, how soon after this, will the car reach the observation tower?
  • 12 min 39 sec
  • 10 min 38 sec
  • 15 min 43 sec
  • 13 min 40 sec
  • 14 min 41 sec
Question 5
5.
    • 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 34°46'. If the distance between the observation point and the top of the radio tower is 1 m, find the distance between the observation point and the foot of the radio tower.
    • From Table of Natural Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      34
      0.5592
      0.5606
      0.5621
      0.5635
      0.5650
      0.5664
      0.5678
      0.5693
      0.5707
      0.5721
      2
      5
      7
      9
      12
    • From Table of Natural Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      34
      0.8290
      0.8281
      0.8271
      0.8261
      0.8251
      0.8241
      0.8231
      0.8221
      0.8211
      0.8202
      2
      3
      5
      7
      8
  • 2.82 m
  • 8.82 m
  • 7.82 m
  • 0.82 m
  • 1.82 m
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)
       
      (
      5
      4
      )
    • .
    • If the height of the
    • tower
    • is
    • 100 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • tower
    • .
  • 125.00 m
  • 139.00 m
  • 108.00 m
  • 107.00 m
Question 7
7.
The angles of depression of two boats from the top of a cliff 180 m high are 30° and 60° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
  • 433.71 m
  • 421.71 m
  • 389.71 m
  • 400.71 m
  • 415.71 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 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 48°1' and 61°3' 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'
      48
      1.1106
      1.1145
      1.1184
      1.1224
      1.1263
      1.1303
      1.1343
      1.1383
      1.1423
      1.1463
      7
      13
      20
      27
      33
    • From Table of Natural Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      61
      1.8040
      1.8115
      1.8190
      1.8265
      1.8341
      1.8418
      1.8495
      1.8572
      1.8650
      1.8728
      13
      26
      38
      51
      64
  • 39.67 m
  • 34.67 m
  • 31.67 m
  • 29.67 m
  • 37.67 m
Question 9
9.
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 9 m, find the height of the flag staff .
  • 5.59 m
  • 7.59 m
  • 6.59 m
  • 8.59 m
  • 4.59 m
Question 10
10.
    • The upper part of a tree is broken into two parts without being detatched. It makes an angle of 51°11' with the ground. The top of the tree touches the ground at a distance of 100 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'
      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
    • From Table of Natural Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      51
      0.6293
      0.6280
      0.6266
      0.6252
      0.6239
      0.6225
      0.6211
      0.6198
      0.6184
      0.9170
      2
      5
      7
      9
      12
  • 279.85 m
  • 288.85 m
  • 300.85 m
  • 283.85 m
  • 271.85 m