Answer
$$A = {50.05^ \circ },\,\,\,\,B = {85.1^ \circ },\,\,\,C = {44.85^ \circ }$$
Work Step by Step
$$\eqalign{
& a = 324{\text{m,}}\,\,\,b = 421{\text{m,}}\,\,\,c = 298{\text{m}} \cr
& {\text{Use the law of cosines to solve for any angle of the triangle}} \cr
& {c^2} = {a^2} + {b^2} - 2ab\cos C \cr
& {\text{Solve for cos }}C \cr
& \cos C = \frac{{{a^2} + {b^2} - {c^2}}}{{2ab}} \cr
& {\text{Substitute}} \cr
& \cos C = \frac{{{{\left( {324} \right)}^2} + {{\left( {421} \right)}^2} - {{\left( {298} \right)}^2}}}{{2\left( {324} \right)\left( {298} \right)}} \cr
& {\text{Use a calculator}} \cr
& \cos C \approx 0.7089711445 \cr
& {\text{Use the inverse cosine function}} \cr
& C \approx {44.85^ \circ } \cr
& \cr
& {\text{Use the Law of sines to find the angle of }}B \cr
& \frac{{\sin B}}{b} = \frac{{\sin C}}{c} \cr
& \sin B = \frac{{b\sin C}}{c} \cr
& \sin B = \frac{{421\sin \left( {{{44.85}^ \circ }} \right)}}{{298}} \cr
& {\text{Use a calculator}} \cr
& \sin B \approx 0.99634758 \cr
& {\text{Use the inverse sine function}} \cr
& B \approx {85.1^ \circ } \cr
& \cr
& {\text{Calculate }}A \cr
& A = {180^ \circ } - B - C \cr
& A = {180^ \circ } - {85.1^ \circ } - {44.85^ \circ } \cr
& A = {50.05^ \circ } \cr
& \cr
& {\text{Answer}} \cr
& A = {50.05^ \circ },\,\,\,\,B = {85.1^ \circ },\,\,\,C = {44.85^ \circ } \cr} $$
