Chapter 10 - Radical Expressions and Equations - 10-1 The Pythagorean Theorem - Practice and Problem-Solving Exercises - Page 603: 9

b=12

The Pythagorean Theorem states that for a right triangle, $a^{2} +b^{2} = c^{2}$. Thus, we plug in the values given for a, b, or c, and then we use these values to find the missing value: $5^{2} + b^{2} = 13^{2} \\\\ 25 + b^{2} =169 \\\\ b^{2} =144 \\\\ b=12$