# Law of Sines - Ambiguous Case

- Author:
- Ken Schwartz

- Topic:
- Sine

The Law of Sines is a formula that can be used to solve all SAA and ASA triangles. It can also be used for SSA triangles, but the triangle resulting from defining angle A and sides a and b depends on the length of side a. If a is too short (a < h), it does not reach the third side c, and no triangle is formed. If a is longer than b, a single triangle results. And if a is between h and b, side a can reach side c in two ways, resulting in two possible triangles.

The lengths of a and b can be changed in the diagram. Length b can be changed by moving point X, and length a can be changed by adjusting the slider. When a < h, no triangle is formed. When a is between h and b, two possible triangles (shown in red and green) can be formed. When a > b, only one triangle is possible (shown all red).