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Sine Law Demonstration by cemccourseware

Sine Law Demonstration by cemccourseware
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2018-10-25 01:41
TriangleTrigonometryGeometric Construction
This example dynamically demonstrates the relationship between the angles and corresponding side lengths of a triangle using the sine law, visually showcasing its application. Core mathematical concepts include the sine law, trigonometric functions, and geometric construction. GeoGebra commands and objects used in the construction are Sequence, Element, Polygon, PointIn, Angle, LaTeX, and TableText. It is suitable for high school mathematics teaching, helping students understand and memorize the sine law and enhancing their spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[C + (0, -0.1), i, Midpoint[A, C]], i, 0.3, π - 0.2, 0.2) → bBottomCirc
  2. Element(bBottomCirc, Length[bBottomCirc]) → bLast
  3. Element(bBottomCirc, 1) → bFirst
  4. Polygon(Union[bBottomCirc, {bLast, (30, y(bLast)), (30, y(bFirst)), bFirst}]) → bRegion
  5. PointIn(bRegion) → B
  6. Polygon(A, C, B) → t1, b, a, c
  7. Angle(A, B, C) → angleB
  8. Angle(C, A, B) → angleA
  9. Angle(B, C, A) → angleC
  10. LaTeX((((("\dfrac{\sin(" * angleA) * ")}{") * a) * "}")) → B4
  11. LaTeX((((("\dfrac{\sin(" * angleB) * ")}{") * b) * "}")) → B5
  12. LaTeX((((("\dfrac{\sin(" * angleC) * ")}{") * c) * "}")) → B6
  13. LaTeX((((("\dfrac{" * sinA) * "}{") * a) * "}")) → D4
  14. LaTeX((((("\dfrac{" * sinB) * "}{") * b) * "}")) → D5
  15. LaTeX((((("\dfrac{" * sinC) * "}{") * c) * "}")) → D6
  16. LaTeX("\hphantom{000000}") → D3
  17. TableText({A3:A6, B3:B6, C3:C6, D3:D6, E3:E6, F3:F6}, "v |1000001 _10001") → ratioTbl
  18. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc
  19. LaTeX((("\textbf{" * ratio) * "}")) → F4
  20. LaTeX((("\textbf{" * ratio) * "}")) → F5
  21. LaTeX((("\textbf{" * ratio) * "}")) → F6