Discovering Trig Ratios: Side-Angle Relationships in Right Triangles

① This interactive GeoGebra example demonstrates the definitions of sine, cosine, and tangent as ratios of sides in a right triangle, allowing users to explore how these ratios depend on the acute angle. ② Core mathematical concepts include trigonometric ratios (sin, cos, tan), right triangles, similar triangles, and the correspondence between angle measures and side-length ratios. ③ Construction details: using GeoGebra commands such as Line, OrthogonalLine, Point, Segment, and Angle, the example builds a right triangle with labeled points A, B, C, D, segments h, i, j, k, and angles α, β, γ; dragging vertices dynamically updates the ratios. ④ Suitable for middle school advanced students or high school beginners learning trigonometry, and for teachers demonstrating the geometric foundation of trig ratios in classroom settings.