$$\eqalign{
& {{AC} \over {\sin B}} = {{AB} \over {\sin C}} = {{BC} \over {\sin A}} \cr
& \Leftrightarrow {{35} \over {\sin 60}} = {{AB} \over {\sin 50}} = {{BC} \over {\sin 70}} = {{35\sqrt 3 } \over 2} \cr
& \Rightarrow \left\{ \matrix{
AB = {{35\sqrt 3 } \over 2}.\sin 50 \simeq 23,22 \hfill \cr
BC = {{35\sqrt 3 } \over 2}.\sin 70 \approx 28,48 \hfill \cr} \right. \cr
& {S_{\Delta ABC}} = {1 \over 2}AC.BC.\sin C \approx {1 \over 2}.35.\sin 50.{{35\sqrt 3 } \over 2}.\sin 70 \approx 381,84 \cr} $$
