# Chapter 10 - Exponents and Radicals - 10.7 The Distance Formula, the Midpoint Formula, and Other Applications - 10.7 Exercise Set - Page 676: 14

$\sqrt{31}\approx5.568 \text{ }cm$

#### Work Step by Step

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 $c=6$ and $a=\sqrt{5} ,$ then \begin{array}{l}\require{cancel} a^2+b^2=c^2 \\\\ (\sqrt{5})^2+b^2=6^2 \\\\ 5+b^2=36 \\\\ b^2=36-5 \\\\ b^2=31 \\\\ b=\sqrt{31} .\end{array} Hence, the other leg is $\sqrt{31}\approx5.568 \text{ }cm$ long.

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