Proof: Cosine Rule 2

This GeoGebra example demonstrates a second geometric proof of the cosine rule (law of cosines), visually showing how the square of one side of a triangle relates to the other two sides and the cosine of the included angle. The core mathematical concept is the cosine rule, which generalizes the Pythagorean theorem to any triangle, involving trigonometric functions (cosine) and algebraic manipulation. The construction uses GeoGebra commands such as Intersect, Point, Segment, Polygon, and Angle to create triangle ABC with sides a, b, c, and adds auxiliary elements like the altitude h, foot X, and text labels to illustrate the proof step by step. Suitable for high school students learning trigonometry and solving triangles, as well as for teachers demonstrating the proof in class or for self-study, helping learners grasp the geometric essence and logical derivation of the cosine rule.