Law of Sines: No, Right, One, or Two Triangles
- Ken Schwartz
Once two sides of a triangle are constructed, four options exist for the third side: Case 1: It is too short to even make a triangle; Case 2: It's just barely long enough to make a right triangle; Case 3: Its length allows two possible triangles: obtuse or acute; Case 4: Its length is so long it can only make an acute triangle.
Select one of the Cases by checking the box (more than one case can be selected at a time). For cases 3 and 4, drag the endpoint so that it lies on the long horizontal side of the triangle. In Case 3, there will be two places to the right of Angle A where the endpoint can be placed, allowing two possible triangles. This is called the "ambiguous case". In Case 4, the point must be placed to the right of Angle A, and only one place works. (If the horizontal side of the triangle were extended to the left of Angle A, then Angle A would cease to exist and this would amount to Case 3 for a different triangle).