Answer
$14 \text{ and } 14\sqrt{2}$
Work Step by Step
Since the acute angle of the right triangle is $45^o,$ then the right triangle is isosceles. Hence, the legs both measure $14$ units.
Let the right triangle have $a$ and $b$ as the legs and $c$ as the hypotenuse. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $
a=14
$ and $
b=14
,$ then
\begin{array}{l}\require{cancel}
a^2+b^2=c^2
\\\\
14^2+14^2=c^2
\\\\
196+196=c^2
\\\\
2(196)=c^2
\\\\
c=\sqrt{196(2)}
\\\\
c=\sqrt{(14)^2\cdot2}
\\\\
c=14\sqrt{2}
.\end{array}
Hence, the missing sides have measure $
14 \text{ and } 14\sqrt{2}
$ units.
