Chapter 10 - Exponents and Radicals - 10.7 The Distance Formula, the Midpoint Formula, and Other Applications - 10.7 Exercise Set - Page 676: 17

$1 \text{ }m$

Let the right triangle have $a$ and $b$ as the legs and $c$ as the hypotenuse. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $ c=\sqrt{2} $ and $ a=1 ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ 1^2+b^2=(\sqrt{2})^2 \\\\ 1+b^2=2 \\\\ b^2=2-1 \\\\ b^2=1 \\\\ b=\sqrt{1} \\\\ b=1 .\end{array} Hence, the other leg is $ 1 \text{ }m $ long.