#### Answer

$9 \text{ and } 9\sqrt{3}$

#### Work Step by Step

Since the given acute angle of the right triangle is $60^o,$ then the other acute angle measures $30^o.$ The side opposite the $30^o$ angle measures $
9
$ (half the given hypotenuse, $18.$)
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=9
$ and $
c=18
,$ then
\begin{array}{l}\require{cancel}
a^2+b^2=c^2
\\\\
9^2+b^2=18^2
\\\\
81+b^2=324
\\\\
b^2=324-81
\\\\
b^2=243
\\\\
b=\sqrt{243}
\\\\
b=\sqrt{81\cdot3}
\\\\
b=\sqrt{(9)^2\cdot3}
\\\\
b=9\sqrt{3}
.\end{array}
Hence, the missing sides have measure $
9 \text{ and } 9\sqrt{3}
$ units.