Answer
$7 \text{ and } 7\sqrt{3}$
Work Step by Step
Since the given acute angle of the right triangle is $30^o,$ then the side opposite this angle measures $
7
$ (half the given hypotenuse, $14.$)
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=7
$ and $
c=14
,$ then
\begin{array}{l}\require{cancel}
a^2+b^2=c^2
\\\\
7^2+b^2=14^2
\\\\
49+b^2=196
\\\\
b^2=196-49
\\\\
b^2=147
\\\\
b=\sqrt{147}
\\\\
b=\sqrt{49\cdot3}
\\\\
b=\sqrt{(7)^2\cdot3}
\\\\
b=7\sqrt{3}
.\end{array}
Hence, the missing sides have measure $
7 \text{ and } 7\sqrt{3}
$ units.