Answer
$$A = {45.39^ \circ },\,\,\,\,C = {20.89^ \circ }$$
Work Step by Step
$$\eqalign{
& B = {113.72^ \circ },\,\,\,\,\,a = 189.6{\text{yd,}}\,\,\,\,b = 243.8{\text{yd}} \cr
& \cr
& {\text{Use the law of sines to find the angle of }}A \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& \sin A = \frac{{a\sin B}}{b} \cr
& \sin A = \frac{{189.6\sin \left( {{{113.72}^ \circ }} \right)}}{{243.8}} \cr
& {\text{Use a calculator}} \cr
& \sin A = 0.71198 \cr
& {\text{Use the inverse sine function}} \cr
& A = {\sin ^{ - 1}}\left( {0.71198} \right) \cr
& A = {45.39^ \circ } \cr
& \cr
& {\text{Calculating }}C \cr
& C = {180^ \circ } - A - B \cr
& C = {180^ \circ } - {45.39^ \circ } - {113.72^ \circ } \cr
& C = {20.89^ \circ } \cr
& \cr
& {\text{Answer}} \cr
& A = {45.39^ \circ },\,\,\,\,C = {20.89^ \circ } \cr} $$
