SSC Board Practice

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SSC Grade X - Applications of Trigonometry
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
    • 45°
    • .
    • If the distance between the point and the foot of the
    • tower
    • is
    • 70 m
    • ,
    • find the distance between
    • the observation point and the top of the
    • tower
    • .
  • 35

    √

    12
    m
  • 70

    √

    2
    m
  • 140
    m
  • 70
    m
  • 140

    √

    3
    m
Question 2
2.
The angle of elevation of the top of a building from the foot of a tower is 45°. 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 90 m, find the height of the building .
  • 56.96 m
  • 48.96 m
  • 46.96 m
  • 54.96 m
  • 51.96 m
Question 3
3.
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 30°. If the height of the building is 20 m, find the height of the flag staff .
  • 45.00 m
  • 43.00 m
  • 40.00 m
  • 37.00 m
  • 35.00 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 14 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?
  • 21 min 15 sec
  • 20 min 14 sec
  • 17 min 11 sec
  • 18 min 12 sec
  • 19 min 8 sec
Question 5
5.
A person, walking 25 m from a point toward a flagpost , observes that its angle of elevation changes from 45° to 60°. Find the height of the flagpost .
  • (
    75
    2

    √

    6
    +
    25
    2

    √

    18
    )
    m
  • (
    75
    4

    √

    6
    +
    75
    4

    √

    2
    )
    m
  • (
    2
    +

    √

    3
    )
    m
  • (
    75
    2
    +
    25
    2

    √

    3
    )
    m
  • 1875
    2
    m
Question 6
6.
    • 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
    • 30°
    • .
    • If the distance between the point and the top of the
    • chimney
    • is
    • 150 m
    • ,
    • find the height of the
    • chimney
    • .
  • 74
    m
  • 75
    m
  • 73
    m
  • 77
    m
  • 76
    m
Question 7
7.
    • 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
    • 30°
    • .
    • If the distance between the point and the foot of the
    • radio tower
    • is
    • 170 m
    • ,
    • find the height of the
    • radio tower
    • .
  • 170
    3

    √

    18
    m
  • 85

    √

    2
    m
  • 170
    3

    √

    3
    m
  • 170
    3
    m
  • 170
    m
Question 8
8.
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 ?
  • ∠f
  • ∠c
  • ∠d
  • ∠e
Question 9
9.
From the top of a light house which is 35 m high from the sea level, the angles of depression of two ships are 60° and 45°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.
  • 17.79 m
  • 11.79 m
  • 14.79 m
  • 19.79 m
  • 9.79 m
Question 10
10.
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 60° and the distance between them is 230 m , find the height of the cliff.
  • 123.82 m
  • 145.82 m
  • 131.82 m
  • 173.82 m
  • 150.82 m