#### Answer

$\sqrt{19}\approx4.359 \text{ }in$

#### 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=\sqrt{20}
$ and $
a=1
,$ then
\begin{array}{l}\require{cancel}
a^2+b^2=c^2
\\\\
1^2+b^2=(\sqrt{20})^2
\\\\
1+b^2=20
\\\\
b^2=20-1
\\\\
b^2=19
\\\\
b=\sqrt{19}
.\end{array}
Hence, the other leg is $
\sqrt{19}\approx4.359 \text{ }in
$ long.