Answer
$$A = {28.55^ \circ },\,\,\,\,B = {53.35^ \circ },\,\,\,\,C = {98.1^ \circ }$$
Work Step by Step
$$\eqalign{
& a = 28{\text{ft,}}\,\,\,b = 47{\text{ft,}}\,\,\,c = 58{\text{ft}} \cr
& {\text{Use the law of cosines to solve for any angle of the triangle}} \cr
& {c^2} = {a^2} + {b^2} - 2ab\cos C \cr
& {\text{Solve for cos }}C \cr
& \cos C = \frac{{{a^2} + {b^2} - {c^2}}}{{2ab}} \cr
& {\text{Substitute}} \cr
& \cos C = \frac{{{{\left( {28} \right)}^2} + {{\left( {47} \right)}^2} - {{\left( {58} \right)}^2}}}{{2\left( {28} \right)\left( {47} \right)}} \cr
& {\text{Use a calculator}} \cr
& \cos C = - \frac{{53}}{{376}} \cr
& {\text{Use the inverse cosine function}} \cr
& C \approx {98.1^ \circ } \cr
& \cr
& {\text{Use the Law of sines to find the angle of }}A \cr
& \frac{{\sin A}}{a} = \frac{{\sin C}}{c} \cr
& \sin A = \frac{{a\sin C}}{c} \cr
& \sin A = \frac{{28\sin \left( {{{98.1}^ \circ }} \right)}}{{58}} \cr
& {\text{Use a calculator}} \cr
& \sin A \approx 0.4779424554 \cr
& {\text{Use the inverse sine function}} \cr
& A = {28.55^ \circ } \cr
& \cr
& {\text{Calculate }}B \cr
& B = {180^ \circ } - A - C \cr
& B = {180^ \circ } - {28.55^ \circ } - {98.1^ \circ } \cr
& B = {37^ \circ } \cr
& \cr
& {\text{Answer}} \cr
& A = {28.55^ \circ },\,\,\,\,B = {53.35^ \circ },\,\,\,\,C = {98.1^ \circ } \cr} $$
