Answer
$$5$$
Work Step by Step
Use the Pythagorean Theorem:
$$c^{2}=a^{2}+b^{2}.$$
Rearrange terms:
$$a^{2}=c^{2}-b^{2}.$$
Substitute in $b=12$ and $c=13:$
$$a^{2}=13^{2}-12^{2}=169-144=25.$$
Take the square root of both sides:
$$\sqrt {a^{2}}=\sqrt {25}$$
$$a=5.$$