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The area rule

The area rule gives the area of a triangle when you know two sides and the angle between them. It follows from the height towards one side being the other side times the sine of the angle. You then do not need to compute the height separately.

T=12 bcsin⁡AT = \tfrac12\,bc\sin Athe area rule

Symbols

TTarea
b, cb,\ ctwo sides
AAthe angle between them°

Example

b=5b = 5, c=7c = 7 and A=60∘A = 60^\circ: T=12⋅5⋅7⋅sin⁡60∘≈15.2T = \tfrac12\cdot 5\cdot 7\cdot\sin 60^\circ \approx 15.2.

The angle must lie between the two sides you use.
Practise trigonometry for free →

← The cosine rule · Linear inequalities →

Part of Mathematics 1T: Trigonometry.