#### Answer

$\sqrt{51}\approx7.141 \text{ }m$

#### 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=10
$ and $
a=7
,$ then
\begin{array}{l}\require{cancel}
a^2+b^2=c^2
\\\\
7^2+b^2=10^2
\\\\
49+b^2=100
\\\\
b^2=100-49
\\\\
b^2=51
\\\\
b=\sqrt{51}
.\end{array}
Hence, the other leg is $
\sqrt{51}\approx7.141 \text{ }m
$ long.