Answer
$$A = {49^ \circ }40',\,\,\,b = 16.1{\text{cm, }}\,c = 25.8{\text{cm}}$$
Work Step by Step
$$\eqalign{
& B = {38^ \circ }40',\,\,\,a = 19.7{\text{cm,}}\,\,\,C = {91^ \circ }40' \cr
& {\text{Find }}A \cr
& A = {180^ \circ } - B - C \cr
& A = {180^ \circ } - {38^ \circ }40' - {91^ \circ }40' \cr
& A = {49^ \circ }40' \cr
& \cr
& {\text{Use the law of sines to find side }}b \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& b = \frac{{a\sin B}}{{\sin A}} \cr
& b = \frac{{19.7\sin \left( {{{38}^ \circ }40'} \right)}}{{\sin \left( {{{49}^ \circ }40'} \right)}} \cr
& {\text{Use a calculator}} \cr
& b = 16.1{\text{cm}} \cr
& \cr
& {\text{Use the law of sines to find side }}c \cr
& \frac{a}{{\sin A}} = \frac{c}{{\sin C}} \cr
& c = \frac{{a\sin C}}{{\sin A}} \cr
& c = \frac{{19.7\sin \left( {{{91}^ \circ }40'} \right)}}{{\sin \left( {{{49}^ \circ }40'} \right)}} \cr
& c = 25.8{\text{cm}} \cr
& \cr
& {\text{Answer}} \cr
& A = {49^ \circ }40',\,\,\,b = 16.1{\text{cm, }}\,c = 25.8{\text{cm}} \cr} $$