Law of Sines (SSA Case): Why It's Ambiguous

This GeoGebra applet dynamically demonstrates the ambiguous case of the Law of Sines when given two sides and a non-included angle (SSA). It visually shows how a fixed side length and angle can produce two possible triangles, one triangle, or no triangle at all, helping students grasp why SSA is not a valid congruence criterion. Core mathematical concepts include the Law of Sines, triangle congruence conditions, solving triangles with multiple solutions, and intersection analysis in geometric construction. The construction uses GeoGebra commands such as Ray, Rotate, Angle, Segment, Circle, and Intersect, involving objects like rays, rotated angles, segments, circles, and intersection points. By adjusting parameters α and side length a, students observe how the number of intersections between the circle and the ray changes, revealing the number of possible solutions. This applet is suitable for high school or early college students studying trigonometry, triangle solving, or geometric construction, and is also an excellent teaching tool for classroom demonstrations to clarify the SSA ambiguity.