Geometric Construction of Trigonometric Ratios for 90°

This example uses a precise geometric setup to demonstrate how trigonometric ratios relate to a right angle (90°). It visualizes the relationship between angle measurement and the corresponding sine, cosine, and tangent interpretations in a geometry context. The construction focuses on foundational trigonometry ideas: defining trigonometric quantities via geometric elements, working with angles in degrees, and highlighting how tangent-line or directional relationships connect to the ratio viewpoint. In GeoGebra, the key build steps come from the construction summary: the commands “Segment”, “Point”, and “Angle” generate the required segments and labeled points (e.g., A, B, C, D) and create angle objects (e.g., α, β) together with text annotations (text1_1, text2_1, etc.) to label the ratios. The auxiliary objects (f, g, h, i, j, k) support the visualization of the tangent/direction-related elements. Suitable for middle school to early high school learning, classroom demonstration, and self-study of trigonometric definitions and right-angle behavior.