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Question

A ladder rests against a wall at an angle α to the horizontal. Its foot is pulled away from the wall through a distance a slides a distance b down the wall making an angle β with the horizontal. Choose the correct option-

A
a=btan(α+β2)
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B
b=atanα+β2
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C
a=bsinα+β2
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D
b=asinα+β2
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Solution

The correct option is A a=btan(α+β2)
InOQS,cosβ=OSQSOS=cosβ

InOPR,cos=ORPROR=cos

a=OSOR=(cosβcos)

InOPR,sin=OPPROP=sin

OQS,sinβ=OQQSOQ=sinβ

b=OPOQ=(sinsinβ)

ab=cosβcossinsinβ=2sin(+β2)sin(β2)2cos(+β2)sin(β2)

ab=tan[+β2]

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