Answer
$$B = 69.1^\circ ,\,\,\,C = 59.7^\circ ,\,\,\,b = 8640{\text{ cm}}$$
Work Step by Step
$$\eqalign{
& A = {\text{51}}.{\text{2}}0^\circ ,\,\,\,c = {\text{7986 cm}},\,\,\,a = {\text{72}}0{\text{8 cm}} \cr
& {\text{Use the law of sines to find the angle of }}C \cr
& \frac{{\sin C}}{c} = \frac{{\sin A}}{a} \cr
& \sin C = \frac{{c\sin A}}{a} \cr
& {\text{Substituting }} \cr
& \sin C = \frac{{{\text{7986}}\sin \left( {{\text{51}}.{\text{2}}0^\circ } \right)}}{{{\text{72}}0{\text{8}}}} \cr
& {\text{Use a calculator}} \cr
& \sin C \approx 0.86345629 \cr
& C \approx {\sin ^{ - 1}}\left( {0.86345629} \right) \cr
& C \approx 59.7^\circ \cr
& \cr
& {\text{Calculate the angle of }}B \cr
& B = 180^\circ - A - C \cr
& B = 180^\circ - {\text{51}}.{\text{2}}0^\circ - 59.7^\circ \cr
& B = 69.1^\circ \cr
& \cr
& {\text{Use the law of sines to find side }}b \cr
& \frac{b}{{\sin B}} = \frac{a}{{\sin A}} \cr
& b = \frac{{{\text{72}}0{\text{8}}\sin \left( {69.1^\circ } \right)}}{{\sin \left( {{\text{51}}.{\text{2}}0^\circ } \right)}} \cr
& b \approx 8640{\text{ cm}} \cr
& \cr
& {\text{Answer}} \cr
& B = 69.1^\circ ,\,\,\,C = 59.7^\circ ,\,\,\,b = 8640{\text{ cm}} \cr} $$
