#### Answer

$9\sqrt{3} \text{ and } 18$

#### 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 this angle is half the hypotenuse. Hence, the hypotenuse is $18.$
The side opposite the $60^o$ angle, $a,$ is $\dfrac{\sqrt{3}}{2}\cdot c,$ where $c$ is the hypotenuse. Hence, \begin{array}{l}\require{cancel}
\dfrac{\sqrt{3}}{2}\cdot c=a
\\\\
\dfrac{\sqrt{3}}{2}\cdot 18=a
\\\\
9\sqrt{3}=a
.\end{array}
Hence, the missing sides have measure $
9\sqrt{3} \text{ and } 18
$ units.