## Algebra: A Combined Approach (4th Edition)

$2\sqrt{131} \text{ } m \text{ OR } \approx 22.9 \text{ } m$
$\bf{\text{Solution Outline:}}$ Use the Pythagorean Theorem to solve for the value of the missing side measurement. $\bf{\text{Solution Details:}}$ Based on the given figure, the missing side is one of the legs of the right triangle. Let $a$ be the missing side measurement. Using the Pythagorean Theorem which is given by $a^2+b^2=c^2,$ with $b= 9$ and $c= 11\sqrt{5} ,$ then \begin{array}{l}\require{cancel} a^2+9^2=(11\sqrt{5})^2 \\\\ a^2+81=121(5) \\\\ a^2+81=605 \\\\ a^2=605-81 \\\\ a^2=524 .\end{array} Taking the principal square root of both sides (since there are no negative side measurement) and simplifying the radical result to \begin{array}{l}\require{cancel} a=\sqrt{524} \\\\ a=\sqrt{4\cdot131} \\\\ a=\sqrt{(2)^2\cdot131} \\\\ a=2\sqrt{131} .\end{array} Hence, the missing side is $2\sqrt{131} \text{ } m \text{ OR } \approx 22.9 \text{ } m .$