Answer
$$A = {36.54^ \circ },\,\,\,a = 28.10{\text{m, }}\,b = 44.17{\text{m}}$$
Work Step by Step
$$\eqalign{
& C = {74.08^ \circ },\,\,\,B = {69.38^ \circ },\,\,\,c = 45.38{\text{m}} \cr
& \cr
& {\text{Use the law of sines to find side }}b \cr
& \frac{c}{{\sin C}} = \frac{b}{{\sin B}} \cr
& b = \frac{{c\sin B}}{{\sin C}} \cr
& b = \frac{{45.38\sin \left( {{{69.38}^ \circ }} \right)}}{{\sin \left( {{{74.08}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& b \approx 44.17{\text{m}} \cr
& \cr
& {\text{Find }}A \cr
& A = {180^ \circ } - B - C \cr
& A = {180^ \circ } - {69.38^ \circ } - {74.08^ \circ } \cr
& A = {36.54^ \circ } \cr
& \cr
& {\text{Use the law of sines to find side }}a \cr
& \frac{a}{{\sin A}} = \frac{c}{{\sin C}} \cr
& a = \frac{{c\sin A}}{{\sin C}} \cr
& a = \frac{{45.38\sin \left( {{{36.54}^ \circ }} \right)}}{{\sin \left( {{{74.08}^ \circ }} \right)}} \cr
& a = 28.10{\text{m}} \cr
& \cr
& {\text{Answer}} \cr
& A = {36.54^ \circ },\,\,\,a = 28.10{\text{m, }}\,b = 44.17{\text{m}} \cr} $$
