## Proof of the Cosine Rule

With a triangle labelled as below

the Cosine Rule states

to prove the rule, drop a perpendicular fromto the side

Pythagoras Theorem gives

Equating these expressions gives

hence

From the above diagram,so

With a triangle labelled as below

the Cosine Rule states

to prove the rule, drop a perpendicular fromto the side

Pythagoras Theorem gives

Equating these expressions gives

hence

From the above diagram,so