Why does height=a (sin C)?

Question

In a random triangle why is it the formula A=ab (sinC)? Why does it work

Answer 1

This formula:  A = ab (sin C) deals with finding the area of

a triangle when knowing two sides of the triangle and the

angle between them:

 

a and b are the sides; C is the angle formed by the

intersection of lines a and b

 

Looking at a height, H, drawn from the endpoint of segment a

to segment b, we could write:  sin C = H / a; therefor we could

say:  a(sinC ) = H

 

If you draw the figure, I think that you will be able to see 

what is taking place.