# Chapter 8 - Right Triangles and Trigonometry - 8-1 The Pythagorean Theorem and It's Converse - Practice and Problem-Solving Exercises - Page 496: 21

5$\sqrt 3$

#### Work Step by Step

The Pythagorean Theorem says that $(leg_{1}) ^{2}$+$(leg_{2})^{2}$=$hypotenuse^{2}$. This formula is more commonly referred to as $a^{2}$+$b^{2}$=$c^{2}$ You are given the lengths of one leg as 5 and the length of the hypotenuse as 10. Substitute 5 in for a and 10 in for c. $a^{2}$+$b^{2}$=$c^{2}$ $5^{2}$+$b^{2}$=$10^{2}$ 25+$b^{2}$=100 Subtract 25 from both sides. $b^{2}$=75 Take the square root of both sides to find the length of the missing side. b=5$\sqrt 3$

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