Intermediate Algebra (6th Edition)

$2\sqrt{10} \text{ } m.$
Using $a^2+b^2=c^2$ (or the Pythagorean Theorem) where a leg is given the measure $3$ meters and the hypotenuse is given the measure $7$ meters, then the other leg, $b$, is equal to \begin{array}{l}\require{cancel} 3^2+b^2=7^2 \\\\ b^2=7^2-3^2 \\\\ b^2=49-9 \\\\ b^2=40 \\\\ b=\sqrt{40} \\\\ b=\sqrt{4\cdot10} \\\\ b=\sqrt{(2)^2\cdot10} \\\\ b=2\sqrt{10} .\end{array} Hence, the unknown side is