Theorem:
If ABC is a triangle with sides a = BC, b = CA, c = AB, then prove that

In figure (i),
A < 90o

In figure (ii),
A > 90o

In figure(iii),
From (i), (ii) and (iii), we conclude that
Similarly, b2 = c2 + a2 - 2 ca cos B

Example:

Suggested answer:




Dividing throughout by 2abc, we get

