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Exploring Trigonometric Ratios by David

Exploring Trigonometric Ratios by David
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2015-07-21 00:54
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the dynamic relationship between side lengths and angles in right triangles, involving core math concepts like trigonometric definitions, similar triangles, and coordinate geometry. It uses GeoGebra commands such as Line, OrthogonalLine, Point, Polygon, Dilate, and Angle for construction, making it suitable for high school mathematics instruction to visually connect trigonometry with geometric figures.

GeoGebra Commands & Parameters

  1. Line(B, C) → d
  2. OrthogonalLine(C, d) → e
  3. Point(e) → A
  4. Polygon(B, C, A) → poly1, a, b, c
  5. Dilate(B, 5, B_1) → B''
  6. Dilate(C, 5, B_1) → C''
  7. Dilate(A, 5, B_1) → A''
  8. Polygon(B'', C'', A'') → poly1', a'', b'', c''
  9. Dilate(B, 3, B_1) → B'
  10. Dilate(C, 3, B_1) → C'
  11. Dilate(A, 3, B_1) → A'
  12. Polygon(B', C', A') → poly1'_1, a', b', c'
  13. Angle(A, C, B) → α
  14. Angle(B, A, C) → β
  15. Angle(A', C', B') → γ
  16. Angle(B', A', C') → δ
  17. Angle(A'', C'', B'') → ε
  18. Angle(B'', A'', C'') → ζ