Introduction to Trigonometric Ratios in Right Triangles

This GeoGebra applet demonstrates that the sine, cosine, and tangent ratios in a right triangle depend only on the measure of the acute angle and are independent of the side lengths. By adjusting the angle and the overall size of the triangle, users can verify that sin, cos, and tan remain constant for a fixed angle. The core mathematical concepts include right triangles, adjacent side, opposite side, hypotenuse, trigonometric ratios (sine, cosine, tangent), angle measurement, and similarity of right triangles. Construction highlights: GeoGebra commands such as Point, Segment, Line, OrthogonalLine, Intersect, Rotate, Angle, and Distance are used to create vertices A, B, C, angles α, β, γ, and labels Adj, Opp, Hyp for the adjacent, opposite, and hypotenuse sides. Suitable for middle school and high school mathematics instruction (grades 7–12) and for independent student exploration of trigonometric definitions and geometric intuition.