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Law of Sines - Ambiguous Case by Brendon

Law of Sines - Ambiguous Case by Brendon
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2015-02-27 00:13
TriangleTrigonometryGeometric Construction
This example demonstrates the ambiguous case of the Law of Sines in triangle geometry, where given two sides and a non-included angle, two distinct triangles may be formed. It involves core concepts like the Law of Sines, triangle solving, and ambiguous case analysis. The construction uses commands such as Line, Segment, Angle, Intersect, Defined, If, OrthogonalLine to create triangles and visualize the ambiguity through sliders and conditional logic. Suitable for high school mathematics education to help students understand the applicability and special cases of the Law of Sines.

GeoGebra Commands & Parameters

  1. Line(A, B_1) → a_1
  2. Segment(A, C) → b
  3. Angle(B_1, A, C) → α
  4. Segment(C, MoveMe) → Sidea
  5. Intersect(Sidea, a_1) → B
  6. Angle(C, B, A) → β
  7. Angle(A, C, MoveMe) → γ
  8. Segment(A, B) → c
  9. Segment(C, B) → a
  10. Defined(β) → d
  11. If(a < h, "No Triangle Possible!") → text6
  12. If(a < h, "No Triangle Possible") → text7
  13. OrthogonalLine(C, a_1) → i
  14. Intersect(a_1, c) → D
  15. Intersect(i, a_1) → E
  16. Segment(E, C) → Altitude
  17. If(a < h, Text["No Triangle Possible!"]) → text8
  18. If(a < h, Text["No Triangle Possible!"]) → text9
  19. If(a < h, Text["No Triangle Possible!"]) → text10_2
  20. If(a < h, Text["No Triangle Possible!"]) → None
  21. Defined(a) → t