Question

# A flag pole $18m$ high casts a shadow $9.6m$ long. Find the distance of the top of the pole from the far end of the shadow.

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Solution

## Let's find the length of $LN$ in the figure.Let $MN=18m$ be the flag pole and its shadow be $LM=9.6m$The distance of the top of the pole,$N$ from the far end, $L$of the shadow is $LN.$From right-angled $∆LMN$,$L{N}^{2}=L{M}^{2}+M{N}^{2}$On applying Pythagoras theorem we obtain⇒$⇒L{N}^{2}={\left(9.6\right)}^{2}+{\left(18\right)}^{2}⇒L{N}^{2}=9.216+324\phantom{\rule{0ex}{0ex}}⇒L{N}^{2}=416.16\phantom{\rule{0ex}{0ex}}⇒L{N}^{}=\sqrt{415.16}=20.4m$Hence, the required distance is $20.4m$

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