Answer
$$A = {112^ \circ }10',\,\,\,\,B = {26^ \circ }30'$$
Work Step by Step
$$\eqalign{
& C = {41^ \circ }20',\,\,\,b = 25.9{\text{m,}}\,\,\,c = 38.4{\text{m}} \cr
& \cr
& {\text{Use the law of sines to find the angle of }}B \cr
& \frac{b}{{\sin B}} = \frac{c}{{\sin C}} \cr
& \sin B = \frac{{b\sin C}}{c} \cr
& \sin B = \frac{{25.9\sin \left( {{{41}^ \circ }20'} \right)}}{{38.4}} \cr
& {\text{Use a calculator}} \cr
& \sin B = 0.4454 \cr
& {\text{Use the inverse sine function}} \cr
& B = {26^ \circ }30' \cr
& \cr
& {\text{Calculating }}A \cr
& A = {180^ \circ } - B - C \cr
& A = {180^ \circ } - {26^ \circ }30' - {41^ \circ }20' \cr
& A = {112^ \circ }10' \cr
& \cr
& {\text{Answer}} \cr
& A = {112^ \circ }10',\,\,\,\,B = {26^ \circ }30' \cr} $$
