Answer
$14\sqrt{3} \text{ and } 28$
Work Step by Step
Since the given acute angle of the right triangle is $30^o,$ then the side opposite this angle is half the hypotenuse. Hence, the hypotenuse is $28.$
The other acute angle measures $60^o.$ The side opposite this 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 28=a
\\\\
14\sqrt{3}=a
.\end{array}
Hence, the missing sides have measure $
14\sqrt{3} \text{ and } 28
$ units.
