Answer
(a) $7.84m$ or $3.25m$;
(b) See explanations.
Work Step by Step
(a) Given $A=\frac{\pi}{8}$, we have two cases: 1. $a=3m$ then $c=\frac{a}{sinA}=\frac{3}{sin\frac{\pi}{8}}\approx7.84m$; case 2: $b=3m$ then $c=\frac{b}{cosA}=\frac{3}{cos\frac{\pi}{8}}\approx3.25m$.
(b) There are two answers because we do not know if the known side is facing the given angle or not.