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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, so that it slides a distance b down the wall making an angle β with the horizontal. Show that
ab=cos αcos βsin βsin α


Solution

To show ab=cos αcos βsin βsin α(1)
cos α=BDDE=ABaDE
cos β=ABAC
sin β=BCAC=EBbAC
sin α=EBDE
Put in (1)

cos αcos βsin βsin α=ABaDEABACEBbACEBDE
DE=AC=Length of ladder
cos αcos βsin βsin α=ABaACABACEBbACEBAC
ABaABACEBbEBAC
=ab=ab

All India Test Series

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