Answer
$$A = {37^ \circ }47',\,\,\,\,C = {93^ \circ }23'$$
Work Step by Step
$$\eqalign{
& B = {48^ \circ }50',\,\,\,a = 3850{\text{in,}}\,\,\,b = 4730{\text{in}} \cr
& \cr
& {\text{Use the law of sines to find the angle of }}A \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& \sin A = \frac{{a\sin B}}{b} \cr
& \sin A = \frac{{3850\sin \left( {{{48}^ \circ }50'} \right)}}{{4730}} \cr
& {\text{Use a calculator}} \cr
& \sin A = 0.612742 \cr
& {\text{Use the inverse sine function}} \cr
& A = {\sin ^{ - 1}}\left( {0.612742} \right) \cr
& A = {37^ \circ }47' \cr
& \cr
& {\text{Calculating }}C \cr
& C = {180^ \circ } - A - B \cr
& C = {180^ \circ } - {37^ \circ }47' - {48^ \circ }50' \cr
& C = {93^ \circ }23' \cr
& \cr
& {\text{Answer}} \cr
& A = {37^ \circ }47',\,\,\,\,C = {93^ \circ }23' \cr} $$
