Answer
$$A = 25.4^\circ ,\,\,\,B = 102.3^\circ ,\,\,\,b = 74.029{\text{yd}}$$
Work Step by Step
$$\eqalign{
& C = {\text{52}}.{\text{3}}^\circ ,a = {\text{32}}.{\text{5 yd}},c = {\text{59}}.{\text{8 yd}} \cr
& {\text{Use the law of sines to find the angle of }}A \cr
& \frac{{\sin A}}{a} = \frac{{\sin C}}{c} \cr
& \sin A = \frac{{a\sin C}}{c} \cr
& {\text{Substituting }} \cr
& \sin A = \frac{{\left( {{\text{32}}.{\text{5}}} \right)\sin \left( {{\text{52}}.{\text{3}}^\circ } \right)}}{{{\text{59}}.{\text{8}}}} \cr
& {\text{Use a calculator}} \cr
& \sin A \approx 0.43 \cr
& A \approx {\sin ^{ - 1}}\left( {0.43} \right) \cr
& A \approx 25.4^\circ \cr
& \cr
& {\text{Calculate the angle of }}B \cr
& B = 180^\circ - A - C \cr
& B = 180^\circ - 25.4^\circ - {\text{52}}.{\text{3}}^\circ \cr
& B = 102.3^\circ \cr
& \cr
& {\text{Use the law of sines to find side }}b \cr
& \frac{b}{{\sin B}} = \frac{a}{{\sin A}} \cr
& b = \frac{{a\sin B}}{{\sin A}} \cr
& b = \frac{{{\text{32}}.{\text{5}}\sin \left( {102.3^\circ } \right)}}{{\sin \left( {25.4^\circ } \right)}} \cr
& b \approx 74.029{\text{yd}} \cr} $$
