MathPlotAI Logo MathPlotAI

Law of Cosines by Leslee Villalobos

Law of Cosines by Leslee Villalobos
Loading the math board and drawing, please wait…
2017-01-14 06:47
TriangleTrigonometryGeometric Construction
This example demonstrates the Law of Cosines, which states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice their product with the cosine of the included angle. Using GeoGebra commands such as Rotate, Angle, Ray, and Segment, the example dynamically illustrates the application of the Law of Cosines. Suitable for middle school and above students to learn trigonometry and geometric construction.

GeoGebra Commands & Parameters

  1. Rotate(A_1, α, C) → A'
  2. Angle(A_1, C, A') → β
  3. Ray(A_1, A') → f
  4. Segment(A_1, C) → g
  5. Ray(C, A') → h
  6. Ray(C, A_1) → i
  7. Point(i) → A
  8. Point(h) → B
  9. Segment(A, B) → j
  10. Segment(C, A) → k
  11. Segment(C, B) → l
  12. OrthogonalLine(C, j) → m
  13. Intersect(m, j) → D
  14. Polygon(A, D, C) → poly1, b, c, e
  15. Polygon(D, C, B) → poly2, d, e_1, b_1
  16. Angle(C, D, A) → γ
  17. Distance(A, D) → a
  18. Distance(D, B) → n
  19. Min(a, n) → o
  20. Circle(D, (0.2 * o)) → p
  21. Segment(C, D) → q
  22. Intersect(p, j) → F, G
  23. Intersect(p, q) → H,
  24. CircleSector(D, G, H) → r
  25. Dilate(C, If[0 < s ≤ 1, 1 - s, 0], D) → B'
  26. Segment(C, B') → t
  27. Rotate(r, If[1.5 < s ≤ 2.5, ((s - 1.5) * π / 2), π / 2], D) → r'
  28. Dilate(D, If[2.5 < s ≤ 3.5, 3.5 - s, 0], A) → E'
  29. Dilate(C, If[2.5 < s ≤ 3.5, 3.5 - s, 0], A) → B'_1
  30. Segment(C, B'_1) → f_1
  31. Segment(D, E') → g_1
  32. Circle(D, 1) → c_1
  33. Intersect(c_1, m, 1) → I
  34. Line(A, m) → h_1
  35. Line(B, m) → i_1
  36. OrthogonalLine(I, m) → j_1
  37. Intersect(h_1, j_1) → J
  38. Intersect(i_1, j_1) → K
  39. Polygon(A, D, C) → poly3, c_2, a_1, d_1
  40. Dilate(D, If[2.5 < s ≤ 3.5, 3.5 - s, 0], B) → D'
  41. Dilate(C, If[2.5 < s ≤ 3.5, 3.5 - s, 0], B) → C'
  42. Segment(C, C') → k_1
  43. Segment(D, D') → l_1
  44. Dilate(A, If[3.5 < s ≤ 4.5, 4.5 - s, 0], J) → A'_1
  45. Dilate(B, If[3.5 < s ≤ 4.5, 4.5 - s, 0], K) → B'_2
  46. Segment(A, A'_1) → m_1
  47. Segment(B, B'_2) → n_1
  48. Dilate(J, If[4.5 < s ≤ 5.5, 5.5 - s, 0], K) → J'
  49. Segment(J, J') → p_1