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Law of Sines, Ambiguous Case (SSA)

Law of Sines, Ambiguous Case (SSA)
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2016-07-09 04:31
TriangleCircleTrigonometryGeometric Construction
This example demonstrates the scenarios under Side-Side-Angle (SSA) conditions where 0, 1, or 2 distinct triangles can be formed, illustrating the ambiguity in triangle construction using the Law of Sines. Key concepts include the Law of Sines, triangle congruence criteria, and geometric constructions. GeoGebra commands like Line, Circle, Intersect, Rotate, and others are used to visualize and analyze the intersection points. Suitable for high school trigonometry and geometry education.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → L
  2. Circle(A, b_1) → c_2
  3. Intersect(c_2, L, 2) → B_1
  4. Rotate(B_1, α_1, A) → C_1
  5. Angle(B_1, A, C_1) → α
  6. Segment(A, C_1) → b
  7. Circle(C_1, a_1) → e
  8. Point(e) → B
  9. Segment(C_1, B) → a
  10. Ray(A, B_1) → g
  11. OrthogonalLine(C_1, xAxis) → h
  12. Intersect(h, g) → D
  13. Segment(C_1, D) → i
  14. Angle(C_1, D, A) → γ
  15. Polygon(A, C_1, B) → poly1, c_1, a_2, b'
  16. Angle(C_1, B, A) → β
  17. Angle(A, C_1, B) → C
  18. Distance(A, B) → distanceAC