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Law of Sines & Area

Law of Sines & Area
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2019-09-24 23:58
TriangleTrigonometryGeometric Construction
This example demonstrates the calculation of triangle area using the Law of Sines. Key math concepts include the Law of Sines, triangle area formulas, and geometric constructions. GeoGebra commands and objects used in the construction are Polygon, Midpoint, Rotate, Segment, Line, OrthogonalLine, Intersect, Dilate, and Angle. Suitable for high school mathematics education to understand and apply the Law of Sines and triangle area calculations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c_2, a, b_3
  2. Midpoint(b_3) → D
  3. Rotate(A, α, D) → A'
  4. Rotate(B, α, D) → B'
  5. Rotate(C, α, D) → C'
  6. Polygon(A', B', C') → poly1', c', a', b'
  7. Segment(A, D) → i
  8. Segment(D, C) → j
  9. Segment(C, B) → k
  10. Segment(B, A) → l
  11. Segment(A', B') → g
  12. Segment(B', C') → m
  13. Line(B, C) → f
  14. Line(B, A) → h_1
  15. Line(A, C) → n
  16. OrthogonalLine(A, f) → p
  17. OrthogonalLine(B, n) → q
  18. OrthogonalLine(C, h_1) → r
  19. Intersect(f, p) → E
  20. Intersect(n, q) → F
  21. Intersect(h_1, r) → G
  22. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], E) → A'_1
  23. Segment(A, A'_1) → height
  24. Polygon(B, E, A) → poly2, a_1, b_1, e
  25. Polygon(E, A, C) → poly3, c_1, e_1, a_2
  26. Angle(A, E, B) → β
  27. Polygon(B, E, A) → poly4, a_3, b_2, e_2
  28. Dilate(B, If[0 < d ≤ 1, 1 - d, 0], E) → B'_1
  29. Dilate(B, If[0 < d ≤ 1, 1 - d, 0], A) → B'_2
  30. Segment(B, B'_1) → h
  31. Segment(B, B'_2) → c
  32. Segment(A, C) → b