Answer
$$B = {18.50^ \circ },\,\,\,a = 239{\text{yd, }}\,c = 230{\text{yd}}$$
Work Step by Step
$$\eqalign{
& A = {87.2^ \circ },\,\,\,b = 75.9{\text{yd}},\,\,\,C = {74.3^ \circ } \cr
& {\text{Find }}B \cr
& B = {180^ \circ } - A - C \cr
& B = {180^ \circ } - {87.2^ \circ } - {74.3^ \circ } \cr
& B = {18.50^ \circ } \cr
& \cr
& {\text{Use the law of sines to find side }}a \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& a = \frac{{b\sin A}}{{\sin B}} \cr
& a = \frac{{75.9\sin \left( {{{87.2}^ \circ }} \right)}}{{\sin \left( {{{18.50}^ \circ }} \right)}} \cr
& {\text{Use a calculator}} \cr
& a = 239{\text{yd}} \cr
& \cr
& {\text{Use the law of sines to find side }}c \cr
& \frac{a}{{\sin A}} = \frac{c}{{\sin C}} \cr
& c = \frac{{a\sin C}}{{\sin A}} \cr
& c = \frac{{239\sin \left( {{{74.3}^ \circ }} \right)}}{{\sin \left( {{{87.2}^ \circ }} \right)}} \cr
& c = 230{\text{yd}} \cr
& \cr
& {\text{Answer}} \cr
& B = {18.50^ \circ },\,\,\,a = 239{\text{yd, }}\,c = 230{\text{yd}} \cr} $$
