EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Some Applications of Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
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
    • cosec
      (-1)
       
      (
      4
      3
      )
    • .
    • If the height of the
    • tower
    • is
    • 20 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • tower
    • .
  • (i)
    21.67 m
  • (ii)
    31.67 m
  • (iii)
    29.67 m
  • (iv)
    23.67 m
  • (v)
    26.67 m
Question 2
2.
    • A
    • chimney
    • stands vertically on the ground.
    • From a point on the ground,
    • the angle of elevation
    • of the top of the
    • chimney
    • is found to be
    • 45°
    • .
    • If the distance between the point and the top of the
    • chimney
    • is
    • 100 m
    • ,
    • find the height of the
    • chimney
    • .
  • (i)
    100
    m
  • (ii)
    50

    √

    2
    m
  • (iii)
    50
    m
  • (iv)
    25

    √

    12
    m
  • (v)
    100

    √

    3
    m
Question 3
3.
    • The upper part of a tree is broken into two parts without being detatched. It makes an angle of 30°34' with the ground. The top of the tree touches the ground at a distance of 130 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'
      30
      0.5774
      0.5797
      0.5820
      0.5844
      0.5867
      0.5890
      0.5914
      0.5938
      0.5961
      0.5985
      4
      8
      12
      16
      20
    • From Table of Natural Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      30
      0.8660
      0.8652
      0.8643
      0.8634
      0.8625
      0.8616
      0.8607
      0.8599
      0.8590
      0.8581
      1
      3
      4
      6
      7
  • (i)
    253.77 m
  • (ii)
    227.77 m
  • (iii)
    239.77 m
  • (iv)
    202.77 m
  • (v)
    220.77 m
Question 4
4.
From the top of a 20 m high building , the angle of elevation of the top of a cable tower is 45° and the angle of depression of its foot is 30°. Find the height of the cable tower.
  • (i)
    49.64 m
  • (ii)
    51.64 m
  • (iii)
    57.64 m
  • (iv)
    54.64 m
  • (v)
    59.64 m
Question 5
5.
    • From the top of a 15 m high building , the angle of elevation of the top of a cable tower is 46°27' and the angle of depression of its foot is 33°16'. Find the height of the cable tower.
    • 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'
      33
      0.6494
      0.6519
      0.6544
      0.6569
      0.6594
      0.6619
      0.6644
      0.6669
      0.6694
      0.6720
      4
      8
      13
      17
      21
  • (i)
    42.05 m
  • (ii)
    34.05 m
  • (iii)
    44.05 m
  • (iv)
    39.05 m
  • (v)
    36.05 m
Question 6
6.
    • An observer 1.4 m tall, is 30 m away from a tower . The angle of elevation of the top of the tower from her eyes is 37°40'. 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'
      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
  • (i)
    29.56 m
  • (ii)
    19.56 m
  • (iii)
    27.56 m
  • (iv)
    24.56 m
  • (v)
    21.56 m
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 51°4'. If the distance between the observation point and the top of the tower is 3 m, find the height of the tower.
    • From Table of Natural Sines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      51
      0.7771
      0.7782
      0.7793
      0.7804
      0.7815
      0.7826
      0.7837
      0.7848
      0.7859
      0.7869
      2
      4
      5
      7
      9
    • 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
  • (i)
    2.33 m
  • (ii)
    4.33 m
  • (iii)
    0.33 m
  • (iv)
    3.33 m
  • (v)
    1.33 m
Question 8
8.
From the top of a light house which is 30 m high from the sea level, the angles of depression of two ships are 45° and 30°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
  • (i)
    24.96 m
  • (ii)
    21.96 m
  • (iii)
    18.96 m
  • (iv)
    16.96 m
  • (v)
    26.96 m
Question 9
9.
    • 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)
       
      (
      6
      7
      )
    • .
    • If the distance between the point and the top of the
    • tower
    • is
    • 40 m
    • ,
    • find the height of the
    • tower
    • .
  • (i)
    39.29 m
  • (ii)
    34.29 m
  • (iii)
    37.29 m
  • (iv)
    31.29 m
  • (v)
    29.29 m
Question 10
10.
    • Two poles of equal height are standing opposite to each other on either side of a road which is 25 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 37°33' and 38°14' 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'
      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'
      38
      0.7813
      0.7841
      0.7869
      0.7898
      0.7926
      0.7954
      0.7983
      0.8012
      0.8040
      0.8069
      5
      9
      14
      19
      23
  • (i)
      • height =
      • 10.73 m
      • , distances away =
      • 13.35 m
      • ,
      • 13.65 m
  • (ii)
      • height =
      • 8.73 m
      • , distances away =
      • 11.35 m
      • ,
      • 11.65 m
  • (iii)
      • height =
      • 9.73 m
      • , distances away =
      • 12.35 m
      • ,
      • 12.65 m
  • (iv)
      • height =
      • 7.73 m
      • , distances away =
      • 10.35 m
      • ,
      • 10.65 m
  • (v)
      • height =
      • 11.73 m
      • , distances away =
      • 14.35 m
      • ,
      • 14.65 m
Question 11
11.
A man in a boat rowing away from a lighthouse 90 m high, takes 2 min to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat.
  • (i)
    0.87 m/sec
  • (ii)
    2.87 m/sec
  • (iii)
    1.87 m/sec
  • (iv)
    8.87 m/sec
  • (v)
    7.87 m/sec
Question 12
12.
    • The angle of elevation of the top of a building from the foot of a tower is 33°24'. The angle of elevation of the top of the tower from the foot of the building is 46°46'. 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'
      33
      0.6494
      0.6519
      0.6544
      0.6569
      0.6594
      0.6619
      0.6644
      0.6669
      0.6694
      0.6720
      4
      8
      13
      17
      21
    • 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
  • (i)
    63.89 m
  • (ii)
    58.89 m
  • (iii)
    55.89 m
  • (iv)
    61.89 m
  • (v)
    53.89 m
Question 13
13.
    • A
    • tower
    • stands vertically on the ground.
    • The height of the
    • tower
    • is
    • 80

      √

      3
      m
    • .
    • The distance between the observation point and its top
    • is
    • 160
      m
    • .
    • Find the angle of elevation.
  • (i)
    30°
  • (ii)
    60°
  • (iii)
    45°
  • (iv)
    105°
  • (v)
    90°
Question 14
14.
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 building is 16 m, find the height of the flag staff .
  • (i)
    8.71 m
  • (ii)
    16.71 m
  • (iii)
    6.71 m
  • (iv)
    14.71 m
  • (v)
    11.71 m
Question 15
15.
The shadow of a vertical tower BA on a level ground is increased by 10 m, when the altitude of the sun changes from 45° to 30°. Find the height of the tower .
  • (i)
    18.66 m
  • (ii)
    16.66 m
  • (iii)
    10.66 m
  • (iv)
    13.66 m
  • (v)
    8.66 m
Question 16
16.
There are two temples one on each bank of a river, just opposite to each other. One of the temples is 120 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 45° and 60° respectively. Find the width of the river .
  • (i)
    66.28 m
  • (ii)
    72.28 m
  • (iii)
    64.28 m
  • (iv)
    69.28 m
  • (v)
    74.28 m
Question 17
17.
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 60°. If the height of the tower is 35 m, find the height of the building .
  • (i)
    16.67 m
  • (ii)
    6.67 m
  • (iii)
    11.67 m
  • (iv)
    8.67 m
  • (v)
    14.67 m
Question 18
18.
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 45°, how soon after this, will the car reach the observation tower?
  • (i)
    9 min 13 sec
  • (ii)
    7 min 11 sec
  • (iii)
    5 min 10 sec
  • (iv)
    10 min 14 sec
  • (v)
    8 min 12 sec
Question 19
19.
From a point 90 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 45° respectively. Find the height of the cliff.
  • (i)
    93.00 m
  • (ii)
    85.00 m
  • (iii)
    87.00 m
  • (iv)
    95.00 m
  • (v)
    90.00 m
Question 20
20.
    • 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 39°49' and the angle of elevation of the top of the building is 24°37'. If the height of the flag staff is 15 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'
      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'
      39
      0.8098
      0.8127
      0.8156
      0.8185
      0.8214
      0.8243
      0.8273
      0.8302
      0.8332
      0.8361
      5
      10
      15
      19
      24
  • (i)
    18.30 m
  • (ii)
    23.30 m
  • (iii)
    15.30 m
  • (iv)
    21.30 m
  • (v)
    13.30 m
Question 21
21.
A boy standing on a vertical cliff in a jungle observes two rest houses in line with him on opposite sides deep in the jungle below. If their angles of depression are 45° and 30° and the distance between them is 225 m , find the height of the cliff.
  • (i)
    79.36 m
  • (ii)
    82.36 m
  • (iii)
    77.36 m
  • (iv)
    85.36 m
  • (v)
    87.36 m
Question 22
22.
If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?
  • (i)
    ∠b
  • (ii)
    ∠c
  • (iii)
    ∠e
  • (iv)
    ∠d
Question 23
23.
An observer 1.8 m tall, is 120 m away from a tower . The angle of elevation of the top of the tower from her eyes is 60°. Find the height of the tower .
  • (i)
    215.65 m
  • (ii)
    184.65 m
  • (iii)
    222.65 m
  • (iv)
    209.65 m
  • (v)
    202.65 m
Question 24
24.
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 ?
  • (i)
    ∠e
  • (ii)
    ∠d
  • (iii)
    ∠c
  • (iv)
    ∠b
Question 25
25.
The angles of depression of two boats from the top of a cliff 90 m high are 45° and 60° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
  • (i)
    43.03 m
  • (ii)
    38.03 m
  • (iii)
    41.03 m
  • (iv)
    33.03 m
  • (v)
    35.03 m
    Assignment Key
  •  1) (v)
  •  2) (ii)
  •  3) (ii)
  •  4) (iv)
  •  5) (iv)
  •  6) (iv)
  •  7) (i)
  •  8) (ii)
  •  9) (ii)
  •  10) (iii)
  •  11) (i)
  •  12) (ii)
  •  13) (ii)
  •  14) (v)
  •  15) (iv)
  •  16) (iv)
  •  17) (iii)
  •  18) (v)
  •  19) (v)
  •  20) (i)
  •  21) (ii)
  •  22) (iv)
  •  23) (iv)
  •  24) (iv)
  •  25) (ii)