Law of Sines:
The Ambiguous Case: SSA
Given two sides and an angle of a potential triangle, there is a possiblity that it forms one, two or no triangle at all. In order to determine the number of solutions for the given situation, we must compare the side opposite the given angle with the minimum length needed to close the triangle (i.e. the perpendicular distance from the baseline to the end of the given segment.) We can find the line by recognizing that this minimum distance must be related to the given angle and side in the following form:

To use this applet, do the following:

Set the sliders to the measurements given in the problems.

Move the endpoint D so that it closes the triangle, how many ways can it do so?