In a triangle, sides $a,b,$ and $c$ are opposite angles $A,B,$ and $C,$ respectively. If $a=35,B=50,$ and $C=60,$ find a formula for $c.$

A$)c=35sin50$

B$)c=\frac{35sin50}{sin60}$

C$)c=\frac{35sin60}{sin70}$

D$)c=\frac{sin70}{35sin50}$

E$)$ None of the above