Answer
$\text{approximately } 13.2 \text{ } cm.$
Work Step by Step
Using $a^2+b^2=c^2$ (or the Pythagorean Theorem) where the legs are given the measures $5\sqrt{3}$ centimeters and $10$ centimeters, the measure of the hypotenuse, $c$, is equal to
\begin{array}{l}\require{cancel}
(5\sqrt{3})^2+(10)^2=c^2
\\\\
25\cdot3+100=c^2
\\\\
75+100=c^2
\\\\
175=c^2
\\\\
c=\sqrt{175}
\\\\
c\approx13.2
.\end{array}
Hence, the unknown side is $
\text{approximately } 13.2 \text{ } cm.
$
