Answer
$C= 44^\circ$
$b \approx14.4$
$c \approx10.5$
Work Step by Step
Step 1. Given angles $A, B$, we can find angle $C$ as:
$C=180^\circ-64^\circ-72^\circ=44^\circ$
Step 2. Using the Law of Sines, we have
$\frac{sinB}{b}=\frac{sinA}{a}$, thus $b=\frac{a\ sinB}{sinA}=\frac{13.6\ sin72^\circ}{sin64^\circ}\approx14.4$
Step 3. Using the Law of Sines, we have
$\frac{sinC}{c}=\frac{sinA}{a}$, thus $c=\frac{a\ sinC}{sinA}=\frac{13.6\ sin44^\circ}{sin64^\circ}\approx10.5$
