Why 1/2 ab sin C

Why 1/2 ab sin C?
Rectangle formula:base x height
Triangle formula:1/2 x base x height

Actually this formula 0.5ab sin C is same formula with basic triangle formula. We ignore 1/2 and base first.

Find height :
sin C = h/a
Height = a x sin C

Triangle formula:
1/2 x height x base
= 0.5 x a x sin C x b
= 1/2 ab sin C
(proven)