sin$\frac{A}{2}$ = sqrt((s-b)$\frac{s-c}{(bc)}$), cos$\frac{A}{2}$ = sqrt$\frac{s(s-a}{(bc)}$), tan$\frac{A}{2}$ = sqrt((s-b)$\frac{s-c}{(s(s-a)}$)). These express half-angle trig ratios entirely in terms of sides (via semi-perimeter). They bridge the gap between side-based and angle-based descriptions of a triangle.