Answer
$4\sqrt{2} \text{ and } 4\sqrt{2}$
Work Step by Step
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.
