Answer
$$49^\circ 26'$$
Work Step by Step
$$\eqalign{
& {\text{Let }}C = {\text{79}}^\circ {\text{2}}0\prime ,c = {\text{97}}.{\text{4 mm}},a = {\text{75}}.{\text{3 mm}} \cr
& {\text{Find }}A,{\text{ use the law of sines}} \cr
& \frac{{\sin A}}{a} = \frac{{\sin C}}{c} \cr
& \sin A = \frac{{a\sin C}}{c} \cr
& \cr
& {\text{Substitute}} \cr
& \sin A = \frac{{\left( {{\text{75}}.{\text{3 mm}}} \right)\sin \left( {{\text{79}}^\circ {\text{2}}0\prime } \right)}}{{{\text{97}}.{\text{4 mm}}}} \cr
& \cr
& {\text{Use a calculator}} \cr
& \sin A \approx 0.7597419373 \cr
& A \approx {\sin ^{ - 1}}\left( {0.7597419373} \right) \cr
& A \approx 49^\circ 26' \cr} $$
