Answer
$A= 36^\circ$, $B= 54^\circ$, and $b= 18\ m$
Work Step by Step
Given $a=13\ m, c=22\ m$, we have $sinA=\frac{a}{c}=\frac{13}{22}$, thus $A=asin(\frac{13}{22})\approx36^\circ$, $B=90^\circ-36^\circ=54^\circ$, and $b=\sqrt {c^2-a^2}=\sqrt {22^2-13^2}\approx18\ m$