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A ladder rests against a wall at an angl...

A ladder rests against a wall at an angle `alpha` to the horizontal, its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle `beta` with the horizontal. Show that `a = b tan 1/2(alpha + beta)`.

Text Solution

Verified by Experts

The correct Answer is:
`a= b tan(alpha + beta)/2`.
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Knowledge Check

  • A ladder rests against a wall at an angle alpha to the horizontal. Its foot is pulled away from the wall through a distance 'a' so that it slides a distance 'b' down the wall making an angle beta with the horizontal, then

    A
    `a=b" tan"(alpha+beta)/(2)`
    B
    `a=b" cot"(alpha+beta)/(2)`
    C
    `a" tan(alpha-beta)/(2)`
    D
    None

  • A ladder rests against a vertical wall at angle alpha to the horizontal . If is foot is pulled away from the wall through a distance 'a' so that it slides a distance 'b' down the wall making the angle beta with the horizontal , then a =

    A
    `b tan ((alpha-beta)/2)`
    B
    `b tan ((alpha+beta)/2)`
    C
    `b cot ((alpha - beta)/2)`
    D
    none of these

  • A ladder rests against a wall at an acute angle alpha to the horizontal. Its foot is pulled away form the wall through a distance 2 m, so that it slides a distance 3 m down the wall making an acute angle beta with the horizontal , then the value of tan (( alpha + beta)/(2)) is

    A
    `3/2`
    B
    `2/3`
    C
    `4/9`
    D
    `9/4`

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