EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Some Applications of Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question 1
1.
A man 1.3 m tall stands at a distance of 2.5 m from a lamp post and casts a shadow of 1.1 m on the ground. Find the height of the lamp post .
  • (i)
    6.25 m
  • (ii)
    5.25 m
  • (iii)
    4.25 m
  • (iv)
    2.25 m
  • (v)
    3.25 m
Question 2
2.
    • 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 foot of the
    • radio tower
    • is
    • 70 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • radio tower
    • .
  • (i)
    141
    m
  • (ii)
    138
    m
  • (iii)
    140
    m
  • (iv)
    143
    m
  • (v)
    139
    m
Question 3
3.
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 50 m, find the height of the building .
  • (i)
    23.87 m
  • (ii)
    28.87 m
  • (iii)
    33.87 m
  • (iv)
    25.87 m
  • (v)
    31.87 m
Question 4
4.
    • A
    • tower
    • stands vertically on the ground.
    • The distance between the observation point and its foot
    • tower
    • is
    • 190

      √

      2
      m
    • .
    • The distance between the observation point and its top
    • is
    • 380
      m
    • .
    • Find the angle of elevation.
  • (i)
    75°
  • (ii)
    60°
  • (iii)
    105°
  • (iv)
    45°
  • (v)
    30°
Question 5
5.
    • 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°43' and the angle of elevation of the top of the building is 23°46'. If the height of the building is 18 m, find the height of the flag staff .
    • 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'
      45
      1.0000
      1.0035
      1.0070
      1.0105
      1.0141
      1.0176
      1.0212
      1.0247
      1.0283
      1.0319
      6
      12
      18
      24
      30
  • (i)
    20.91 m
  • (ii)
    26.91 m
  • (iii)
    18.91 m
  • (iv)
    23.91 m
  • (v)
    28.91 m
Question 6
6.
    • 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 34°30' and 46°37' 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'
      34
      0.6745
      0.6771
      0.6796
      0.6822
      0.6847
      0.6873
      0.6899
      0.6924
      0.6930
      0.6976
      4
      9
      13
      17
      22
    • 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)
      • height =
      • 13.5 m
      • , distances away =
      • 12.81 m
      • ,
      • 19.19 m
  • (ii)
      • height =
      • 11.5 m
      • , distances away =
      • 10.81 m
      • ,
      • 17.19 m
  • (iii)
      • height =
      • 10.5 m
      • , distances away =
      • 9.81 m
      • ,
      • 16.19 m
  • (iv)
      • height =
      • 12.5 m
      • , distances away =
      • 11.81 m
      • ,
      • 18.19 m
  • (v)
      • height =
      • 14.5 m
      • , distances away =
      • 13.81 m
      • ,
      • 20.19 m
Question 7
7.
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)
    ∠c
  • (ii)
    ∠d
  • (iii)
    ∠e
  • (iv)
    ∠b
Question 8
8.
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 height of the other temple.
  • (i)
    45.72 m
  • (ii)
    53.72 m
  • (iii)
    55.72 m
  • (iv)
    50.72 m
  • (v)
    47.72 m
Question 9
9.
    • 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 50°22' and 70°30' 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'
      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 Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      70
      2.7475
      2.7625
      2.7776
      2.7929
      2.8083
      2.8239
      2.8397
      2.8556
      2.8716
      2.8878
      26
      52
      78
      104
      133
  • (i)
    45.49 m
  • (ii)
    39.49 m
  • (iii)
    42.49 m
  • (iv)
    47.49 m
  • (v)
    37.49 m
Question 10
10.
    • From the top of a light house which is 60 m high from the sea level, the angles of depression of two ships are 48°37' and 22°11'. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
    • 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'
      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
  • (i)
    91.27 m
  • (ii)
    94.27 m
  • (iii)
    89.27 m
  • (iv)
    99.27 m
  • (v)
    97.27 m
Question 11
11.
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)
    ∠a
  • (ii)
    ∠b
  • (iii)
    ∠d
  • (iv)
    ∠c
Question 12
12.
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 11 m, find the height of the flag staff .
  • (i)
    9.05 m
  • (ii)
    10.05 m
  • (iii)
    8.05 m
  • (iv)
    7.05 m
  • (v)
    6.05 m
Question 13
13.
    • 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
    • cot
      (-1)
       
      (
      1
      4
      )
    • .
    • If the height of the
    • tower
    • is
    • 80 m
    • ,
    • find the distance between
    • the observation point and the foot of the
    • tower
    • .
  • (i)
    17.00 m
  • (ii)
    23.00 m
  • (iii)
    25.00 m
  • (iv)
    15.00 m
  • (v)
    20.00 m
Question 14
14.
    • A
    • building
    • stands vertically on the ground.
    • From a point on the ground,
    • the angle of elevation
    • of the top of the
    • building
    • is found to be
    • 60°
    • .
    • If the distance between the point and the top of the
    • building
    • is
    • 130 m
    • ,
    • find the height of the
    • building
    • .
  • (i)
    65
    m
  • (ii)
    195
    2

    √

    2
    m
  • (iii)
    65

    √

    3
    m
  • (iv)
    195
    m
  • (v)
    65

    √

    18
    m
Question 15
15.
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 15 min for the angle of depression to change from 30° to 60°, how soon after this, will the car reach the observation tower?
  • (i)
    9 min 33 sec
  • (ii)
    4 min 27 sec
  • (iii)
    6 min 29 sec
  • (iv)
    8 min 31 sec
  • (v)
    7 min 30 sec
Question 16
16.
The angles of depression of two boats from the top of a cliff 170 m high are 60° and 30° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
  • (i)
    196.30 m
  • (ii)
    212.30 m
  • (iii)
    191.30 m
  • (iv)
    213.30 m
  • (v)
    178.30 m
Question 17
17.
The shadow of a vertical tower BA on a level ground is increased by 20 m, when the altitude of the sun changes from 60° to 30°. Find the height of the tower .
  • (i)
    22.32 m
  • (ii)
    12.32 m
  • (iii)
    20.32 m
  • (iv)
    17.32 m
  • (v)
    14.32 m
Question 18
18.
A person, walking 10 m from a point toward a flagpost , observes that its angle of elevation changes from 45° to 60°. Find the height of the flagpost .
  • (i)
    (
    15
    2

    √

    6
    +
    15
    2

    √

    2
    )
    m
  • (ii)
    150
    m
  • (iii)
    (
    15
    +
    5

    √

    3
    )
    m
  • (iv)
    (
    2
    +

    √

    3
    )
    m
  • (v)
    (
    15

    √

    6
    +
    5

    √

    18
    )
    m
Question 19
19.
    • The upper part of a tree is broken into two parts without being detatched. It makes an angle of 40°20' with the ground. The top of the tree touches the ground at a distance of 190 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'
      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 Cosines
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      40
      0.7660
      0.7649
      0.7638
      0.7627
      0.7615
      0.7604
      0.7593
      0.7581
      0.7570
      0.7559
      2
      4
      6
      7
      9
  • (i)
    413.57 m
  • (ii)
    436.57 m
  • (iii)
    387.57 m
  • (iv)
    410.57 m
  • (v)
    395.57 m
Question 20
20.
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 145 m , find the height of the cliff.
  • (i)
    48.08 m
  • (ii)
    53.08 m
  • (iii)
    56.08 m
  • (iv)
    58.08 m
  • (v)
    50.08 m
Question 21
21.
    • 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 35°14' and the angle of elevation of the top of the building is 30°5'. If the height of the flag staff is 16 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'
      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 Tangents
      x°
      0'
      6'
      12'
      18'
      24'
      30'
      36'
      42'
      48'
      54'
      1'
      2'
      3'
      4'
      5'
      35
      0.7002
      0.7028
      0.7054
      0.7080
      0.7107
      0.7133
      0.7159
      0.7186
      0.7212
      0.7239
      4
      9
      13
      17
      22
  • (i)
    78.05 m
  • (ii)
    76.05 m
  • (iii)
    68.05 m
  • (iv)
    73.05 m
  • (v)
    70.05 m
Question 22
22.
An observer 1.6 m tall, is 100 m away from a tower . The angle of elevation of the top of the tower from her eyes is 45°. Find the height of the tower .
  • (i)
    126.60 m
  • (ii)
    113.60 m
  • (iii)
    101.60 m
  • (iv)
    95.60 m
  • (v)
    74.60 m
Question 23
23.
A man in a boat rowing away from a lighthouse 30 m high, takes 3 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.
  • (i)
    8.07 m/sec
  • (ii)
    0.07 m/sec
  • (iii)
    1.07 m/sec
  • (iv)
    2.07 m/sec
  • (v)
    7.07 m/sec
Question 24
24.
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 17 m, find the height of the building .
  • (i)
    23.22 m
  • (ii)
    28.22 m
  • (iii)
    26.22 m
  • (iv)
    20.22 m
  • (v)
    18.22 m
Question 25
25.
From the top of a 9 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 30°. Find the height of the cable tower.
  • (i)
    39.00 m
  • (ii)
    33.00 m
  • (iii)
    36.00 m
  • (iv)
    41.00 m
  • (v)
    31.00 m
    Assignment Key
  •  1) (iii)
  •  2) (iii)
  •  3) (ii)
  •  4) (iv)
  •  5) (iv)
  •  6) (iv)
  •  7) (iv)
  •  8) (iv)
  •  9) (iii)
  •  10) (ii)
  •  11) (iv)
  •  12) (iii)
  •  13) (v)
  •  14) (iii)
  •  15) (v)
  •  16) (i)
  •  17) (iv)
  •  18) (iii)
  •  19) (iv)
  •  20) (ii)
  •  21) (iv)
  •  22) (iii)
  •  23) (ii)
  •  24) (i)
  •  25) (iii)