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# Redon is $6 \mathrm{ft} 2 \mathrm{in}$. tall, and his shadow is $4 \mathrm{ft} 1 \mathrm{in}$. long. At the same time, a building casts a shadow that is $19 \mathrm{ft} 10 \mathrm{in}$. long. Estimate the height of the building.

Solution

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Write a proportion to find the height of the building :

$\begin{gather*} \frac{6\text{ ft }2\text{ in.}}{h}=\frac{4\text{ ft }1\text{ in.}}{19\text{ ft }10\text{ in.}}\\ \frac{74\text{ in.}}{h}=\frac{49\text{ in.}}{238\text{ in.}} \end{gather*}$

Cross-multiply:

$\begin{gather*} 74\cdot238=h\cdot49\\ 17612=49h. \end{gather*}$

Divide both sides by $49$ :

$\begin{gather*} h=359.4285..\approx359.43\text{ in.}\\ h=29\text{ ft }11.43{ in.} \end{gather*}$

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