Trigonometric formula for the area

Knowing two sides of a triangle and the included angle, the area is worked out at once with a trigonometric formula.

Property — Trigonometric formula for the area

The area of a triangle $ABC$ is: $S = \tfrac{1}{2}\,bc\sin\widehat{A} = \tfrac{1}{2}\,ac\sin\widehat{B} = \tfrac{1}{2}\,ab\sin\widehat{C}.$ “The area is half the product of two sides times the sine of the included angle.”

The triangle with its circumscribed circle of radius $R$.

Links

Topics: Triangle trigonometry
Concepts: Triangle area · Triangle solving
Functions: Sine
Skills: Using formulae