Math

Ambiguous case.

Definition

A situation in triangle solving (SSA — two sides and a non-included angle) where the given information can produce zero, one, or two valid triangles. This occurs when using the Law of Sines with the arrangement side-side-angle.

Examples

Real-world.

  • 1 Given a = 8, b = 12, and angle A = 30°, there are two possible triangles because the side opposite the given angle is shorter than the other given side but longer than a·sin(A)
  • 2 If the side opposite the given angle is shorter than the height (a < b·sin A), no triangle exists
Key Fact

SSA can give 0, 1, or 2 triangles — check if a < b·sin(A), a = b·sin(A), or a > b·sin(A)

Studied in

1 unit use this concept.