To prove A = 1/2•ab•sinC
What is sinC ... it's the opposite over the hypotenuse, so call sinC as h/a
Now, A = 1/2 • ab • h/a
The a's cancel, leaving A = 1/2 • b • h or one-half the base times the height, the standard formula for area of a triangle
Is that good enough proof?
.