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Sine Law Case II (Ambiguous Case)

Sine Law Case II (Ambiguous Case)
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2012-04-13 22:55
TriangleTrigonometryGeometric Construction
In collections Grade 12 Calculus & Vectors MCV4U1
This example demonstrates the ambiguous case of the Sine Law in triangle solving. It involves core math concepts like the Sine Law and the ambiguity in triangle solutions. The construction uses GeoGebra commands/objects such as Intersect, Circle, Point, Ray, Rotate, Angle, and Segment. Suitable for high school mathematics teaching or self-learning to understand the application of the Sine Law in different scenarios.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → T
  2. Circle(T, a) → c
  3. Point(xAxis) → B_1
  4. Ray(T, B_1) → d
  5. Rotate(B_1, B, T) → B'
  6. Angle(B_1, T, B') → α
  7. Segment(B', T) → e
  8. Intersect(c, e, 1) → C
  9. Circle(C, b) → f
  10. Intersect(f, d, 1) → A'
  11. Intersect(f, d, 2) → A
  12. Segment(C, A') → g
  13. Segment(C, A) → h
  14. Segment(T, A') → i
  15. Segment(T, A) → j
  16. Segment(C, T) → k
  17. Angle(C, A', T) → β
  18. Angle(C, A, T) → γ