Tuesday, February 10, 2009

Law of Sines: how it has been derived.

It can be observed that:

\sin A = \frac{h}{b}\text{ and } \sin B = \frac{h}{a}.

Therefore

h = b\,(\sin A) = a\,(\sin B)

and

\frac{a}{\sin A} = \frac{b}{\sin B}.

Doing the same thing with the line drawn between angle A and side a will yield:

\frac{b}{\sin B} = \frac{c}{\sin C}.
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