Consider each case and determine whether there is sufficient information to solve the triangle using the law of sines.


Three sides are known.

Key Concepts

Law of Sines

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides and angles. This relationship is expressed as a/b = sin(A)/sin(B) = c/sin(C). It is particularly useful for solving triangles when we have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Triangle Properties

A triangle is defined by three sides and three angles, and the sum of the angles in any triangle is always 180 degrees. When three sides are known, the triangle can be solved using the Law of Cosines to find the angles first, which can then be used with the Law of Sines if needed. Understanding these properties is crucial for determining the feasibility of solving a triangle.

Ambiguous Case of SSA

The SSA (Side-Side-Angle) condition can lead to an ambiguous situation where two different triangles may be formed, one triangle, or no triangle at all. This ambiguity arises because knowing two sides and a non-included angle does not guarantee a unique triangle. Recognizing this case is essential when applying the Law of Sines to ensure accurate solutions.