Answer
$$A = 47.65^\circ ,\,\,B = 73.96^\circ ,\,\,\,C = 58.39^\circ $$
Work Step by Step
$$\eqalign{
& a = {\text{94}}.{\text{6 yd}},b = {\text{123 yd}},c = {\text{1}}0{\text{9 yd}} \cr
& \cr
& {\text{Use the Law of cosines to find any Angle}} \cr
& {c^2} = {a^2} + {b^2} - 2ab\cos C \cr
& \cos C = \frac{{{a^2} + {b^2} - {c^2}}}{{2ab}} \cr
& \cos C = \frac{{{{\left( {{\text{94}}.{\text{6}}} \right)}^2} + {{\left( {{\text{123}}} \right)}^2} - {{\left( {109} \right)}^2}}}{{2\left( {{\text{94}}.{\text{6}}} \right)\left( {{\text{123}}} \right)}} \cr
& {\text{Use a calculator}} \cr
& \cos C \approx 0.5241221059 \cr
& C \approx {\cos ^{ - 1}}\left( {0.5241221059} \right) \cr
& C \approx 58.39^\circ \cr
& \cr
& {\text{Calculate the angle }}A{\text{ using the law of sines}} \cr
& \frac{{\sin A}}{a} = \frac{{\sin C}}{c} \cr
& \sin A = \frac{{a\sin C}}{c} \cr
& \sin A = \frac{{{\text{94}}.{\text{6}}\sin \left( {58.39^\circ } \right)}}{{{\text{1}}0{\text{9}}}} \cr
& {\text{Use a calculator}} \cr
& \sin A = 0.7391258285 \cr
& A \approx {\sin ^{ - 1}}\left( {0.7391258285} \right) \cr
& A \approx 47.65^\circ \cr
& \cr
& {\text{Calculate }}B \cr
& B = {180^ \circ } - A - C \cr
& B = {180^ \circ } - 47.65^\circ - 58.39^\circ \cr
& B = 73.96^\circ \cr
& \cr
& {\text{Answer}} \cr
& A = 47.65^\circ ,\,\,B = 73.96^\circ ,\,\,\,C = 58.39^\circ \cr} $$
