Dynamic Trigonometric Ratios in a Right Triangle

This GeoGebra example dynamically demonstrates a right triangle whose angle and side lengths can be changed, allowing students to observe how the adjacent, opposite, and hypotenuse ratios respond in real time. It covers core concepts such as sine, cosine, tangent, angle-side relationships, and the proportional meaning of trigonometric ratios in unit-circle and tangent constructions. The construction uses Intersect, Circle, Tangent, Rotate, Angle, Ray, and Segment commands to create points A, B, C, and A′, segments AB, c, b, and d, angles α, β, and γ, and labeled objects such as Adjacent, Opposite, and Hypotenuse, with multiple text objects displaying ratios and explanations. It is suitable for middle-school or high-school mathematics lessons introducing trigonometry, building geometric intuition, and supporting inquiry-based or interactive demonstrations.