Answer
$a=9.7,B=13^\circ,C=145^\circ$
Work Step by Step
Step 1. Based on the given conditions, using the Law of Cosines, we have
$a^2=b^2+c^2-2bc\ cosA=(6)^2+(15)^2-2(6)(15)cos(22^\circ)\approx94.11$, thus $c\approx\sqrt {94.11}\approx9.7$
Step 2. To find the unknown angles, using the Law of Sines, we have
$\frac{SinB}{b}=\frac{SinA}{a}$, $SinB=\frac{6}{9.7}sin(22^\circ)\approx0.2317$, thus $B=sin^{-1}(0.2317)\approx13^\circ$
Step 3. We can find the angle as
$C=180^\circ-22^\circ132^\circ=145^\circ$
Step 4. We solved the triangle with $a=9.7,B=13^\circ,C=145^\circ$
