Answer
$$41.7^\circ $$
Work Step by Step
$$\eqalign{
& {\text{Let }}C = {\text{51}}.{\text{3}}^\circ ,c = {\text{68}}.{\text{3 m}},b = {\text{58}}.{\text{2 m}} \cr
& \cr
& {\text{Find }}B,{\text{ use the law of sines}} \cr
& \frac{{\sin B}}{b} = \frac{{\sin C}}{c} \cr
& \sin B = \frac{{b\sin C}}{c} \cr
& \cr
& {\text{Substitute}} \cr
& \sin B = \frac{{\left( {{\text{58}}.{\text{2 m}}} \right)\sin \left( {{\text{51}}.{\text{3}}^\circ } \right)}}{{{\text{68}}.{\text{3 m}}}} \cr
& \cr
& {\text{Use a calculator}} \cr
& \sin B = 0.6650226897 \cr
& B = {\sin ^{ - 1}}\left( {0.6650226897} \right) \cr
& B \approx 41.7^\circ \cr} $$
