Answer
$$B = {30^ \circ }$$
Work Step by Step
$$\eqalign{
& {\text{From the triangle we know that:}} \cr
& AC = 3,\,\,\,\,\,BC = 3\sqrt 2 ,\,\,\,\,A = {45^ \circ },\,\,\,\,BC = ? \cr
& \cr
& {\text{Use the law of sines to find the angle of }}B \cr
& \frac{{BC}}{{\sin A}} = \frac{{AC}}{{\sin B}} \cr
& {\text{Substituting }} \cr
& \frac{{3\sqrt 2 }}{{\sin {{45}^ \circ }}} = \frac{3}{{\sin B}} \cr
& {\text{Solve for }}B \cr
& \sin B = \frac{{3\sin {{45}^ \circ }}}{{3\sqrt 2 }} \cr
& {\text{Simplify, recall that }}\sin {45^ \circ } = \frac{{\sqrt 2 }}{2} \cr
& \sin B = \frac{{3\left( {\sqrt 2 /2} \right)}}{{3\sqrt 2 }} \cr
& \sin B = \frac{1}{2} \cr
& ,{\text{then}} \cr
& B = {30^ \circ } \cr} $$
