Law of Sines Proof

This example dynamically demonstrates the geometric proof of the Law of Sines in a triangle, showing the equality of the ratios of the lengths of sides to the sines of their opposite angles. The core mathematical concepts involved include the Law of Sines, triangle geometry, similar triangles, and trigonometric functions. The construction uses GeoGebra commands such as Polygon, OrthogonalLine, Intersect, Angle, Segment, and LaTeX to create the triangle, perpendiculars, altitudes, and sine values of the angles, with dynamic adjustments to illustrate the theorem's generality. Suitable for high school mathematics students and teachers to understand the proof method and geometric meaning of the Law of Sines.