Answer
$\sqrt{3} \text{ }yd$
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=2
$ and $
a=1
,$ then
\begin{array}{l}\require{cancel}
a^2+b^2=c^2
\\\\
1^2+b^2=2^2
\\\\
1+b^2=4
\\\\
b^2=4-1
\\\\
b^2=3
\\\\
b=\sqrt{3}
.\end{array}
Hence, the other leg is $
\sqrt{3} \text{ }yd
$ long.