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Redon is 6ft2in6 \mathrm{ft} 2 \mathrm{in}. tall, and his shadow is 4ft1in4 \mathrm{ft} 1 \mathrm{in}. long. At the same time, a building casts a shadow that is 19ft10in19 \mathrm{ft} 10 \mathrm{in}. long. Estimate the height of the building.

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Write a proportion to find the height of the building :

6 ft 2 in.h=4 ft 1 in.19 ft 10 in.74 in.h=49 in.238 in.\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:

74238=h4917612=49h.\begin{gather*} 74\cdot238=h\cdot49\\ 17612=49h. \end{gather*}

Divide both sides by 4949 :

h=359.4285..359.43 in.h=29 ft 11.43in.\begin{gather*} h=359.4285..\approx359.43\text{ in.}\\ h=29\text{ ft }11.43{ in.} \end{gather*}

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