Skowhegan Area High School
 Parallelograms
 Ambiguous Sine Law (SSA)
In this situation, two cars are racing through a rally course at very high speeds. The blue car, is being driven by Dante, and the red car is being driven by Gonzalez. Gonzalez has the option of taking two different paths. One leads to the water and the other path leads to certain doom for a broken down motorist. Since Gonzalez and Dante had just left math class, even at high speeds, they thought that this was an interesting use of the Ambiguous Sine Law!

The situation is represented by the diagram below:
In this situation, we are given angle A, and we also know the lengths of sides c and a. Both lines, a, have the same distance. So, we must know the remaining dimensions of the triangle, because of SAS. But do we??? Gonzalez could drive on either of the a paths and it would therefore be unclear which triangle would be formed in this situation. This possibility of two triangles, given two sides and the angle not included, is called the Ambiguous Sine Law.