Law of Sines Visualization: Dynamic Triangle Exploration

This applet demonstrates the geometric meaning of the Law of Sines — in any triangle, the ratio of any side length to the sine of its opposite angle is constant (a/sin A = b/sin B = c/sin C). Through a draggable dynamic triangle, students can intuitively observe the constant relationship between side lengths and sines of opposite angles. Core mathematical concepts include the Law of Sines, triangle angle sum, and trigonometric ratios. Construction highlights: Using Segment command to construct sides AB=c, BC=a, AC=b; Angle command to mark interior angles α, β, γ; Circle command to draw circumcircle; Intersect command to determine points on circle; OrthogonalLine to construct altitudes and verify orthocenter properties. Suitable for middle school to high school mathematics teaching, theorem exploration in trigonometry chapters, geometric construction demonstration, or inquiry-based learning activities.