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Ambiguous Case of Law of Sines

Ambiguous Case of Law of Sines
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2017-04-19 04:11
AngleTrigonometryGeometric Construction
This example illustrates the ambiguous case of the Law of Sines. It involves core mathematical concepts such as the sine law in trigonometry. By using GeoGebra commands like Rotate, Angle, Line, Segment, Point, etc., it clearly demonstrates the two possible solutions when given two angles and a non-included side. Suitable for high school mathematics education and students learning the Law of Sines.

GeoGebra Commands & Parameters

  1. Rotate(A_1, α, X) → Y
  2. Angle(A_1, X, Y) → β
  3. Line(X, A_1) → f
  4. Segment(X, Y) → g
  5. Point(Circle[Y, YZ]) → Z
  6. Segment(Y, Z) → h
  7. OrthogonalLine(Y, f) → i
  8. Intersect(f, i) → D
  9. Segment(Y, D) → j
  10. Intersect(f, j) → E
  11. Distance(Y, E) → distanceA'E
  12. Distance(Y, Z) → distanceA'C
  13. Distance(X, Y) → distanceBA
  14. Intersect(f, j) → A
  15. Ray(X, A) → k