Sine Law Proof with Labels (Dynamic Geometry)

This GeoGebra example provides an interactive visual proof of the Sine Law (a/sinα = b/sinβ = c/sinγ) within a dynamic triangle. It demonstrates how the ratio of each side to the sine of its opposite angle is constant and equal to the diameter of the circumcircle. Core concepts include triangle side-angle relationships, trigonometric ratios, and the circumcircle. The construction uses commands such as Segment, Polygon, OrthogonalLine, Angle, Distance, Line, Point, and Intersect to build triangle ABC, draw altitudes, measure angles and side lengths, and display labeled text (TextAC, TextBC, TextAB) for clarity. It also constructs the circumcircle and auxiliary lines to reveal the proof's key proportional relationships. Suitable for high school students learning trigonometry and triangle geometry, this resource serves as an effective teaching aid for classroom demonstrations or self-paced exploration of the Sine Law's geometric foundation.