Answer
$${\text{No such triangle exists}}$$
Work Step by Step
$$\eqalign{
& B = {\text{72}}.{\text{2}}^\circ ,b = {\text{78}}.{\text{3 m}},c = {\text{145 m}} \cr
& \cr
& {\text{Use the law of sines to find the angle of }}C \cr
& \frac{{\sin C}}{c} = \frac{{\sin B}}{b} \cr
& \sin C = \frac{{c\sin B}}{b} \cr
& \sin C = \frac{{145\sin \left( {{\text{72}}.{\text{2}}^\circ } \right)}}{{{\text{78}}.{\text{3}}}} \cr
& {\text{Use a calculator}} \cr
& \sin C = 1.7632 \cr
& {\text{The }}\sin C{\text{ cannot be }} > 1,{\text{ then No such triangle exists}} \cr} $$
