Proof of the Sine Rule
The Sine Rule states that for the triangle labelled as below,
To prove it, start by dropping a perpendicular from a vertex to cut the opposite side at right angles, say fromto b. Label this perpendicular
Thenso
(1)
![](/a-level-maths/C2/proof-of-the-sine-rule-html-4e63807e.gif)
![](/a-level-maths/C2/proof-of-the-sine-rule-html-12b6fb15.gif)
so
Combine this with (1) to obtain