SAS Triangle Construction: 6-Unit, 57°, 7-Unit Solution

This example demonstrates the construction and solution of a triangle given two side lengths and their included angle (SAS: 6 units, 57°, 7 units) using GeoGebra. Core mathematical concepts include SAS triangle congruence, the Law of Cosines, angle rotation, segment-ray intersection, and planar geometric construction. The construction uses Point to establish vertices A and B, Segment to draw sides a, b, and c, Rotate and Angle to set the 57° included angle α, Ray to create auxiliary rays, and Circle together with Intersect to locate the third vertex C, producing related objects such as B′, d, and e. It is suitable for middle-school plane geometry and high-school trigonometry introductions, serving as a classroom demonstration of SAS uniqueness, the geometric meaning of the Law of Cosines, and dynamic geometry construction.