Answer
$4 \text{ }m$
Work Step by Step
Let the right triangle have $a$ and $b$ as the legs and $c$ as the hypotenuse. Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with $
c=8
$ and $
a=4\sqrt{3}
,$ then
\begin{array}{l}\require{cancel}
a^2+b^2=c^2
\\\\
(4\sqrt{3})^2+b^2=8^2
\\\\
16(3)+b^2=64
\\\\
48+b^2=64
\\\\
b^2=64-48
\\\\
b^2=16
\\\\
b=\sqrt{16}
\\\\
b=4
.\end{array}
Hence, the other leg is $
4 \text{ }m
$ long.
