Law+of+Sines--Ambiguous+Case

The ambiguous case When using the law of sines to solve triangles, under special conditions there exists an ambiguous case where two separate triangles can be constructed (i.e., there are two different possible solutions to the triangle). Given a general triangle //ABC//, the following conditions would need to be fulfilled for the case to be ambiguous: Given all of the above premises are true, the angle //B// may be acute or obtuse; meaning, one of the following is true: OR
 * The only information known about the triangle is the angle //A// and the sides //a// and //b//, where the angle //A// is not the included angle of the two sides (in the above image, the angle //C// is the included angle).
 * The angle //A// is acute (i.e., A < 90°).
 * The side //a// is shorter than the side //b// (i.e., //a// < //b//).
 * The side //a// is longer than the altitude of a right angled triangle with angle //A// and hypotenuse //b// (i.e., //a// > //b// sin //A//).