Answer
$10\text{ and } 10\sqrt{3}\approx17.321$
Work Step by Step
Let $a$ be the the side opposite the $30^o$ of the given right triangle. By the properties of a $30-60-90-$degree triangle, this side is half the hypotenuse. Hence $a=10.$ Let $c$ be the hypotenuse and $a,b$ be the legs of the right triangle. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, where $c=20$ and $a=10,$ then
\begin{array}{l}\require{cancel}
a^2+b^2=c^2
\\\\
10^2+b^2=20^2
\\\\
100+b^2=400
\\\\
b^2=400-100
\\\\
b^2=300
\\\\
b=\sqrt{300}
\\\\
b=\sqrt{100\cdot3}
\\\\
b=\sqrt{(10)^2\cdot3}
\\\\
b=10\sqrt{3}
.\end{array}
Hence, the missing measurements are $
10\text{ and } 10\sqrt{3}\approx17.321
$ units.
