Exploring Right Triangle Ratios by Nicole Hafele

① This interactive GeoGebra example dynamically demonstrates how, in a right triangle, the ratios of the opposite side, adjacent side, and hypotenuse (i.e., sine, cosine, tangent) remain constant for a fixed acute angle, even as the triangle is resized or rotated. ② Core mathematical concepts include right triangle side-angle relationships, definitions of trigonometric functions (sin, cos, tan), similarity of triangles, and proportional reasoning. ③ Construction highlights: using GeoGebra commands such as Segment, Point, Rotate, Angle, Line, and Intersect, the example builds a right triangle with labeled vertices (A, B, C) and sides (opp, adj, c), and includes adjustable angle objects (α, β, γ) to explore how changing an acute angle affects the side ratios. ④ Suitable for upper middle school through high school students, this resource is ideal for introducing trigonometry from a geometric perspective, supporting classroom demonstrations or self-guided exploration to bridge visual intuition and formal definitions.