Ambiguous Case

In this activity, segments AC and AB have fixed lengths. Use the slider to adjust the measure of angle B, which is also fixed. Then, drag point A along the circle to explore different triangle possibilities.
  • Can you create more than one triangle using the two given side lengths and one given angle?
  • What does this reveal about using the Law of Sines when you know two sides and a non-included angle (SSA)?
  • Try adjusting the distance between point B and point C. How does this change the number of triangles you can form?
Adapted from Kathryn Brenneman http://www.geogebratube.org/student/m23248.