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Ambiguous Case of the Law of Sines by Jaime Reichlen

Ambiguous Case of the Law of Sines by Jaime Reichlen
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2015-11-24 02:06
TriangleAngleTrigonometryGeometric Construction
This example demonstrates the ambiguous case of the Law of Sines, where given two sides and a non-included angle, the triangle construction may yield one, two, or no solutions. It involves core concepts like the Law of Sines, triangle solving, and geometric construction. The construction uses GeoGebra commands such as Intersect, Point, Ray, Rotate, Angle, Line, Circle, OrthogonalLine, and Segment. Suitable for high school mathematics education to understand special cases in applying the Law of Sines.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A_1
  2. Point(xAxis) → G
  3. Point(yAxis) → H
  4. Ray(A_1, G) → c
  5. Rotate(G, AngleA°, A_1) → G'
  6. Angle(G, A_1, G') → α
  7. Line(A_1, G') → d
  8. Circle(A_1, b_1) → e
  9. Intersect(e, d, 2) → C
  10. OrthogonalLine(C, c) → f
  11. Intersect(c, f) → D
  12. Circle(C, a_1) → g
  13. Intersect(g, c) → B_2, B_1
  14. Segment(D, C) → h
  15. Segment(C, B_2) → i
  16. Segment(C, B_1) → j
  17. Segment(A_1, C) → k
  18. Segment(A_1, B_2) → l
  19. Segment(A_1, B_1) → m
  20. Angle(C, D, A_1) → β
  21. Angle(C, B_2, A_1) → γ
  22. Angle(C, B_1, A_1) → δ