Answer
$5\sqrt{7}
\text{ }
cm
\text{ OR }
\approx 13.2
\text{ }
cm$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Pythagorean Theorem to solve for the value of the missing side measurement.
$\bf{\text{Solution Details:}}$
Based on the given figure, the missing side is the hypotenuse, $c,$ of the right triangle. Using the Pythagorean Theorem which is given by $c^=a^2+b^2,$ with $a=
5\sqrt{3}
$ and $b=
10
,$ then
\begin{array}{l}\require{cancel}
c^2=(5\sqrt{3})^2+10^2
\\\\
c^2=25(3)+100
\\\\
c^2=75+100
\\\\
c^2=175
.\end{array}
Taking the principal square root of both sides (since there are no negative side measurement) and simplifying the radical result to
\begin{array}{l}\require{cancel}
c=\sqrt{175}
\\\\
c=\sqrt{25\cdot7}
\\\\
c=\sqrt{(5)^2\cdot7}
\\\\
c=5\sqrt{7}
.\end{array}
Hence, the missing side is $
5\sqrt{7}
\text{ }
cm
\text{ OR }
\approx 13.2
\text{ }
cm
.$
