Answer
$${\text{No such triangle exists}}$$
Work Step by Step
$$\eqalign{
& B = {74.3^ \circ },\,\,\,a = 859{\text{m,}}\,\,\,b = 783{\text{m}} \cr
& \cr
& {\text{Use the law of sines to find the angle of }}A \cr
& \frac{a}{{\sin A}} = \frac{b}{{\sin B}} \cr
& \sin A = \frac{{a\sin B}}{b} \cr
& \sin A = \frac{{859\sin \left( {{{74.3}^ \circ }} \right)}}{{783}} \cr
& {\text{Use a calculator}} \cr
& \sin A = 1.056 \cr
& {\text{The }}\sin A{\text{ cannot be }} > 1,{\text{ then No such triangle exists}} \cr} $$
