## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$4\sqrt{2} \text{ and } 4\sqrt{2}$
Since the given acute angle of the right triangle is $45^o,$ then the the legs ($a$ and $a$), measure $\dfrac{\sqrt{2}}{2}\cdot c,$ where $c$ is the hypotenuse. Hence, the legs measure \begin{array}{l}\require{cancel} \dfrac{\sqrt{2}}{2}\cdot c=a \\\\ \dfrac{\sqrt{2}}{2}\cdot 8=a \\\\ 4\sqrt{2}=a \\\\ a=4\sqrt{2} .\end{array} Hence, the missing sides have measure $4\sqrt{2} \text{ and } 4\sqrt{2}$ units.