Law of sines

Math

Definition

A proportion relating the sides of a triangle to the sines of their opposite angles. It is used to solve triangles when you know two angles and a side (AAS/ASA) or two sides and a non-included angle (SSA, the ambiguous case).

Examples

  • Finding a missing side when two angles and one side are known
  • Solving the ambiguous case where two triangles may be possible
  • Determining the height of a building using angles measured from two different points
Key Fact

a/sin(A) = b/sin(B) = c/sin(C)

Related Terms

Law of cosines Ambiguous case Solving right triangles Sine cosine tangent

Study This Concept

Practice law of sines with free review games in these units:

Trigonometry Unit 7: Law of Sines and Cosines