Answer
$$A = 60.92^\circ ,\,\,B = 30.38^\circ ,\,\,\,a = 98.25{\text{m}}$$
Work Step by Step
$$\eqalign{
& C = {\text{88}}.{\text{7}}0^\circ ,\,\,\,\,b = {\text{56}}.{\text{87 m}},\,\,\,c = {\text{112}}.{\text{4 m}} \cr
& {\text{Use the law of sines to find the angle of }}B \cr
& \frac{{\sin B}}{b} = \frac{{\sin C}}{c} \cr
& \sin B = \frac{{b\sin C}}{c} \cr
& {\text{Substituting }} \cr
& \sin B = \frac{{{\text{56}}.{\text{87}}\sin \left( {{\text{88}}.{\text{7}}0^\circ } \right)}}{{{\text{112}}.{\text{4}}}} \cr
& {\text{Use a calculator}} \cr
& \sin B \approx 0.5058306245 \cr
& B \approx {\sin ^{ - 1}}\left( {0.5058306245} \right) \cr
& B \approx 30.38^\circ \cr
& \cr
& {\text{Calculate the angle of }}A \cr
& A = 180^\circ - B - C \cr
& A = 180^\circ - 30.38^\circ - {\text{88}}.{\text{7}}0^\circ \cr
& A = 60.92^\circ \cr
& \cr
& {\text{Use the law of sines to find side }}a \cr
& \frac{a}{{\sin A}} = \frac{c}{{\sin C}} \cr
& a = \frac{{c\sin A}}{{\sin C}} \cr
& a = \frac{{{\text{112}}.{\text{4}}\sin \left( {60.92^\circ } \right)}}{{\sin \left( {{\text{88}}.{\text{7}}0^\circ } \right)}} \cr
& a \approx 98.25{\text{m}} \cr
& \cr
& {\text{Answer}} \cr
& A = 60.92^\circ ,\,\,B = 30.38^\circ ,\,\,\,a = 98.25{\text{m}} \cr} $$
