## Precalculus (10th Edition)

$4$
The Pythagorean Theorem says that for a right triangle (if $z$ is the hypotenuse and $x,y$ are the other sides): $x^2+y^2=z^2$. Hence here if we denote the unknown length with $x$: $x^2+3^2=5^2\\ x^2+9=25\\ x^2=25-9\\ x^2=16\\ x=\pm\sqrt{16}\\ x=\pm4$ Since a side length is positive, then $x=4$.