Answer
$B= 27.5^\circ$, $b= 6.6\ m$, and $c= 14.3\ m$
Work Step by Step
Given $A=62.5^\circ, a=12.7\ m$, we have $B=90.0^\circ-62.5^\circ=27.5^\circ$, $b=a\ tanB=12.7tan(27.5^\circ)\approx6.6\ m$, and $c=\frac{a}{sinA}=\frac{12.7}{sin(62.5^\circ)}\approx14.3\ m$
