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Sine and Cosine Rules, and Triangle Area Proofs

Sine and Cosine Rules, and Triangle Area Proofs
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2019-08-13 23:56
TriangleVectorTrigonometryGeometric Construction
This example uses GeoGebra to demonstrate the Sine Rule, Cosine Rule, and their applications in calculating the area of a triangle. Key mathematical concepts include trigonometric functions and triangle area formulas. Using commands like Line, Segment, Polygon, Angle, and Vector, the example provides a visual proof of the rules. Suitable for GCSE, IGCSE, and A-Level students.

GeoGebra Commands & Parameters

  1. Line(A, C) → a
  2. Segment(B, A) → b
  3. Segment(B, C) → c
  4. Segment(C, A) → d
  5. OrthogonalLine(B, a) → e
  6. Intersect(a, e) → D
  7. Segment(B, D) → f
  8. Segment(D, A) → g
  9. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  10. Angle(B, D, C) → α
  11. Angle(A, D, B) → β
  12. Angle(D, A, B) → γ
  13. Angle(B, C, D) → δ
  14. Segment(D, A) → j
  15. Segment(D, C) → k
  16. Vector(E, F) → u
  17. Vector(G, H) → v