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

Question

A ladder rests against a wall at an angle &#x3B1; 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 &#x3B2; with the horizontal. Show that

Philoid · Accepted Answer

In the fig let the length of ladder is h (m)

In ∆AEB

Sin α =

_{AE = h Sin α}

Cos α =

_{BE = h Cos α}

In ∆DEC

Sin β =

_{DE = h Sin β}

Cos β =

_{CE = h Cos β}

_Now

=

= Proved