Answer
$$B = {109.95^ \circ },\,\,\,a = 27{\text{m}},\,\,\,\,c = 21.4{\text{m}}$$
Work Step by Step
$$\eqalign{
& A = {39.70^ \circ },\,\,\,C = {30.35^ \circ }{\text{,}}\,\,\,b = 39.74{\text{m}} \cr
& \cr
& {\text{Find }}B \cr
& B = {180^ \circ } - A - C \cr
& B = {180^ \circ } - {39.70^ \circ } - {30.35^ \circ } \cr
& B = {109.95^ \circ } \cr
& \cr
& {\text{Use the law of sines to find side }}a \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& a = \frac{{b\sin A}}{{\sin B}} \cr
& a = \frac{{39.74\sin \left( {{{39.70}^ \circ }} \right)}}{{\sin \left( {{{109.95}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& a = 27{\text{m}} \cr
& \cr
& {\text{Use the law of sines to find side }}c \cr
& \frac{c}{{\sin C}} = \frac{b}{{\sin B}} \cr
& c = \frac{{b\sin C}}{{\sin B}} \cr
& c = \frac{{39.74\sin \left( {{{30.35}^ \circ }} \right)}}{{\sin \left( {{{109.95}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& c = 21.4{\text{m}} \cr
& \cr
& {\text{Answer}} \cr
& B = {109.95^ \circ },\,\,\,a = 27{\text{m}},\,\,\,\,c = 21.4{\text{m}} \cr} $$
