Answer
$${\text{No such triangle exists}}$$
Work Step by Step
$$\eqalign{
& C = {\text{68}}.{\text{5}}^\circ ,c = {\text{258 cm}},b = {\text{386 cm}} \cr
& {\text{Use the law of sines to find the angle of }}B \cr
& \frac{{\sin B}}{b} = \frac{{\sin C}}{c} \cr
& \sin B = \frac{{b\sin C}}{c} \cr
& \sin B = \frac{{{\text{386}}\sin \left( {68.5^\circ } \right)}}{{{\text{258}}}} \cr
& {\text{Use a calculator}} \cr
& \sin B \approx 1.3920 \cr
& {\text{The }}\sin B{\text{ cannot be }} > 1,{\text{ then No such triangle exists}} \cr} $$
