Chapter 10 - Radical Expressions and Equations - 10-1 The Pythagorean Theorem - Practice and Problem-Solving Exercises - Page 603: 20

b=4

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: $.9^{2} + b^{2} = 4.1^{2} \\\\ .81+ b^{2} =16.81 \\\\ b^{2} =16 \\\\ b=4$