Interactive Verification of Law of Sines and Cosines

①This example demonstrates the numerical verification of the Law of Sines and the Law of Cosines using a dynamic triangle, where dragging vertices updates side lengths and angles in real time. ②Core mathematical concepts include the Law of Sines (a/sinα = b/sinβ = c/sinγ) and the Law of Cosines (c² = a² + b² - 2ab·cosγ), along with the triangle angle sum property. ③Construction details: using GeoGebra commands Polygon to create triangle ABC and Angle to mark interior angles α, β, γ; side lengths a, b, c and angle measures are used to compute both sides of the theorem equations, with dynamic updates via vertex dragging or sliders. ④Suitable for high school or early college students to grasp the geometric meaning of trigonometric identities, and for teachers as a classroom demonstration tool to visually compare theorem applicability across different triangle shapes.