Chapter 10 - Radical Expressions and Equations - 10-1 The Pythagorean Theorem - Practice and Problem-Solving Exercises - Page 603: 19

c=8.5

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: $4^{2} + 7.5^{2} = c^{2} \\\\ 72.25=c^{2} \\\\ c=8.5$