Height and Distance


  1. A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression of 30°. After some time, the angle of depression becomes 60°. The distance (in m) traveled by the car during this time is :









  1. View Hint View Answer Discuss in Forum

    Let us draw the figure from the given question.
    C = Initial point and
    D = Final point
    AB = Tower = 100 m
    Let CD be x m.
    From ΔABD,


    Correct Option: B

    Let us draw the figure from the given question.
    C = Initial point and
    D = Final point
    AB = Tower = 100 m
    Let CD be x m.
    From ΔABD,

    tan 60° = AB
    BD

    3 = 100
    BD

    BD = 100 m
    3

    From ΔABC,

    tan 30° = AB
    BC

    1
    =
    100
    3100 + x
    3

    100 + x = 100 √3
    3

    x = 100 √3 - 100
    3

    x = 300 - 100=200=200 √3m
    3
    3
    3
    The distance (in m) travelled by the car during this time is 200 √3 m
    3



  1. sin A
    +
    sin A
    is ( 0° < A < 90° ) .
    1 + cos A1 - cos A









  1. View Hint View Answer Discuss in Forum

    As per given question , we have

    sin A
    +
    sin A
    1 + cos A1 - cos A

    Correct Option: A

    As per given question , we have

    sin A
    +
    sin A
    1 + cos A1 - cos A

    sin A
    +
    sin A
    =
    sin A( 1 - cos A ) + sin A( 1 + cos A )
    1 + cos A1 - cos A
    ( 1 + cos A )( 1 - cos A )

    = sin A - sin A cos A + sin A sin A cos A
    1 + cos2 A

    = 2 sin A = 2 cosec A
    sin2 A

    sin A
    +
    sin A
    = 2cosec A
    1 + cos A1 - cos A



  1. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is









  1. View Hint View Answer Discuss in Forum

    Let AB be the wall and BC be the ladder.
    Then, ∠ ACB = 60° and AC = 4.6 m.


    Correct Option: D

    Let AB be the wall and BC be the ladder.
    Then, ∠ ACB = 60° and AC = 4.6 m.

    AC/BC = cos 60° = 1/2
    BC = 2 x AC
    = (2 x 4.6) m
    = 9.2 m.