Answer
$$A = {65.6^ \circ },\,\,\,b = 1.94{\text{cm}},\,\,\,\,c = 2.72{\text{cm}}$$
Work Step by Step
$$\eqalign{
& C = {71.83^ \circ },\,\,\,B = {42.57^ \circ }{\text{,}}\,\,\,a = 2.614{\text{cm}} \cr
& \cr
& {\text{Find }}A \cr
& A = {180^ \circ } - B - C \cr
& A = {180^ \circ } - {42.57^ \circ } - {71.83^ \circ } \cr
& A = {65.6^ \circ } \cr
& \cr
& {\text{Use the law of sines to find side }}b \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& b = \frac{{a\sin B}}{{\sin A}} \cr
& b = \frac{{2.614\sin \left( {{{42.57}^ \circ }} \right)}}{{\sin \left( {{{65.6}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& b = 1.94{\text{cm}} \cr
& \cr
& {\text{Use the law of sines to find side }}c \cr
& \frac{c}{{\sin C}} = \frac{b}{{\sin B}} \cr
& c = \frac{{b\sin C}}{{\sin B}} \cr
& c = \frac{{1.94\sin \left( {{{71.83}^ \circ }} \right)}}{{\sin \left( {{{42.57}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& c = 2.72{\text{cm}} \cr
& \cr
& {\text{Answer}} \cr
& A = {65.6^ \circ },\,\,\,b = 1.94{\text{cm}},\,\,\,\,c = 2.72{\text{cm}} \cr} $$
