Answer
$$A = {33.56^ \circ },\,\,\,\,B = {50.7^ \circ },\,\,\,C = {95.74^ \circ }$$
Work Step by Step
$$\eqalign{
& {\text{From the triangle we have:}} \cr
& a = 5,\,\,\,b = 7{\text{ and }}c = 9 \cr
& \cr
& {\text{Use the law of cosines to solve for any angle of the triangle}} \cr
& {c^2} = {a^2} + {b^2} - 2ab\cos C \cr
& {\text{Solve for cos }}C \cr
& \cos C = \frac{{{a^2} + {b^2} - {c^2}}}{{2ab}} \cr
& {\text{Substitute}} \cr
& \cos C = \frac{{{{\left( 5 \right)}^2} + {{\left( 7 \right)}^2} - {{\left( 9 \right)}^2}}}{{2\left( 5 \right)\left( 7 \right)}} \cr
& {\text{Use a calculator}} \cr
& \cos C = - \frac{1}{{10}} \cr
& {\text{Use the inverse cosine function}} \cr
& C \approx {95.74^ \circ } \cr
& \cr
& {\text{Use the Law of sines to find the angle of }}B \cr
& \frac{{\sin B}}{b} = \frac{{\sin C}}{c} \cr
& \sin B = \frac{{b\sin C}}{c} \cr
& \sin B = \frac{{7\sin \left( {{{95.74}^ \circ }} \right)}}{9} \cr
& {\text{Use a calculator}} \cr
& \sin B \approx 0.7738779916 \cr
& {\text{Use the inverse sine function}} \cr
& B \approx {50.7^ \circ } \cr
& \cr
& {\text{Calculate }}A \cr
& A = {180^ \circ } - B - C \cr
& A = {180^ \circ } - {50.7^ \circ } - {95.74^ \circ } \cr
& A = {33.56^ \circ } \cr
& \cr
& {\text{Answer}} \cr
& A = {33.56^ \circ },\,\,\,\,B = {50.7^ \circ },\,\,\,C = {95.74^ \circ } \cr} $$
