Trigonometry
Intermediate

Law of Sines

Relates sides of any triangle to the sines of opposite angles.

Formula

asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Variables

a,b,cSides
A,B,COpposite angles

Example

If a = 7, A = 30°, B = 45°: b = 7·sin45°/sin30° ≈ 9.9.

Did You Know?

The law of sines lets surveyors and astronomers find distances to places they can never physically reach.

law of sinestriangle