Consider any triangle (see figure). Define #sin theta = h/c#, show that the area of triangle is #A_Delta = 1/2 (b*c) sintheta# where #b and c# are any two sides of the traingle that make the angle #theta#?

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Answer 1 · 2016-10-09T16:19:35

See below.

It is well know that

#A_Delta = 1/2 b h = 1/2 b h c/c = 1/2b c (h/c) = 1/2b c sin theta#

the same regarding angle #hat(ACB)#

#A_Delta = 1/2 b h = 1/2 b h a/a = 1/2b a (h/a) = 1/2b a sin beta#

Also can be established

# 1/2b c sin theta = 1/2b a sin beta->sin theta/a=sin beta/c#