Ambiguous CaseAdjust the angle using the slider, then drag the side lengths to find out how many triangles are possible in the various cases. Note that when sin(alpha)*BD/DE > 1, no triangle is possible. When it equals exactly one, a single (right) triangle is possible. When the quantity is less than one, AND DE < BD, two triangles are possible (the ambiguous case), while when DE > BD, only one triangle is possible (the other one is on the wrong side of angle alpha.
Dave Matthews, March 20, 2007, Created with GeoGebra |