Exploring Trigonometric Ratios: Side-Angle Relationships in Right Triangles

① This interactive GeoGebra example dynamically demonstrates how the sine, cosine, and tangent ratios of an acute angle in a right triangle relate to the side lengths. ② Core mathematical concepts include the definitions of trigonometric ratios (opposite/hypotenuse, adjacent/hypotenuse, opposite/adjacent), properties of similar triangles, and the correspondence between angle measures and ratio values. ③ Construction details: using GeoGebra commands Ray, Point, OrthogonalLine, Intersect, Segment, and Angle, the example builds a right triangle with key objects A, C, a, B, b, E, c, D, ED, α, AD, and AE; dragging a point changes the angle α and updates the ratios in real time. ④ Suitable for upper middle school or lower high school students learning introductory trigonometry, and for teachers to illustrate the geometric meaning of trigonometric ratios, laying a foundation for solving triangles and graphing trigonometric functions.