SSC Board Practice

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SSC Grade X - Applications of Trigonometry
Question 1
1.
Two vertical poles are on either side of a road. A 20 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 30° with the pole and when it is turned to rest against another pole, it makes an angle of 45° with the road. Find the width of the road.
  • 28.46 m
  • 31.46 m
  • 34.46 m
  • 36.46 m
  • 26.46 m
Question 2
2.
The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60° with the ground. The top of the tree touches the ground at a distance of 180 m from the foot of the tree . Find the height of the tree before it was broken.
  • 699.78 m
  • 671.78 m
  • 656.78 m
  • 683.78 m
  • 657.78 m
Question 3
3.
    • 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
    • 45°
    • .
    • If the distance between the point and the top of the
    • radio tower
    • is
    • 100 m
    • ,
    • find the distance between
    • the observation point and the foot of the
    • radio tower
    • .
  • 50

    √

    2
    m
  • 100

    √

    3
    m
  • 100
    m
  • 50
    m
  • 25

    √

    12
    m
Question 4
4.
    • 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
    • 30 m
    • ,
    • find the height of the
    • chimney
    • .
  • 30
    m
  • 15
    m
  • 15

    √

    2
    m
  • 30

    √

    3
    m
  • 15
    2

    √

    12
    m
Question 5
5.
The angles of depression of two boats from the top of a cliff 160 m high are 30° and 45° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .
  • 94.14 m
  • 117.14 m
  • 130.14 m
  • 102.14 m
  • 125.14 m
Question 6
6.
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 ?
  • ∠e
  • ∠f
  • ∠d
  • ∠c
Question 7
7.
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 65 m, find the height of the building .
  • 37.53 m
  • 32.53 m
  • 42.53 m
  • 40.53 m
  • 34.53 m
Question 8
8.
Two boys are on opposite sides of a tower of 170 m height. They measure the angle of elevation of the top of the tower as 30° and 60° respectively. Find the distance between the two boys.
  • 340

    √

    2
    m
  • 680
    3
    m
  • 680
    3

    √

    3
    m
  • 680
    3

    √

    18
    m
  • 680
    m
Question 9
9.
The angles of depression of two boats from the top of a cliff 120 m high are 60° and 45° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .
  • 189.29 m
  • 164.29 m
  • 203.29 m
  • 212.29 m
  • 187.29 m
Question 10
10.
A person, walking 15 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 45°. Find the height of the flagpost .
  • (
    45
    4

    √

    2
    +
    15
    4

    √

    6
    )
    m
  • (
    15
    2

    √

    3
    +
    15
    2
    )
    m
  • (
    15
    2

    √

    18
    +
    15
    2

    √

    6
    )
    m
  • 225
    2
    m
  • (
    2
    +

    √

    3
    )
    m