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Calculating Heights and Distances

A ladder 15...

Question

A ladder $15 m$ long reaches a window which is $9 m$ above the ground on one side of a street. keeping its foot at the same point , the ladder is turned to the other side of the street to reach a window $12 m$ height. Find the width of the street.

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Solution

In ΔDCE using Pythagoras,
$D C^{2} + C E^{2} = D E^{2}$
where $D C = 9 m a n d D E = 15 m$
we get $C E = 12 m$
Similarly find BE using Pythagoras in $Δ A B E w e g e t B E = 9 m$ .
Hence, $B C = B E + E C = 12 + 9 = 21 m$

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