MathPlotAI Logo MathPlotAI

30-60-90 Special Right Triangle Exploration

30-60-90 Special Right Triangle Exploration
Loading the math board and drawing, please wait…
2019-02-25 07:13
TriangleTrigonometryGeometric Construction
This example demonstrates the properties and construction of the 30-60-90 special right triangle. Key mathematical concepts include trigonometry and geometric construction. Using commands like rotation, angle measurement, and segment construction in GeoGebra, students can explore the relationships between side ratios and angles. Suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. Ray(B, C) → f
  2. OrthogonalLine(C, f) → g
  3. Rotate(C, π / 3, B) → B'
  4. Angle(C, B, B') → α
  5. Ray(B, B') → h
  6. Intersect(g, h) → A
  7. Segment(B, C) → i
  8. Segment(C, A) → j
  9. Segment(B, A) → k
  10. Polygon(B, C, A) → poly1, c_1, a, b
  11. Circle(A, (0.2 * i)) → e
  12. Intersect(e, k) → D,
  13. Intersect(e, j) → E,
  14. CircleSector(A, D, E) → d
  15. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], B) → C'
  16. Vector(A, C') → u
  17. Translate(d, u) → d'
  18. Rotate(d', If[1 < l ≤ 2, (((l - 1) * 2) * π / 3), (2 * π / 3)], B) → d''
  19. Dilate(A, If[2 < l ≤ 3, 3 - l, 0], B) → C'_1
  20. Vector(A, C'_1) → v
  21. Translate(d, v) → d'_1
  22. Rotate(d'_1, If[3 < l ≤ 4, (((-(l - 3)) * 7) * π / 6), (-7 * π / 6)], B) → p
  23. Dilate(A, If[4 < l ≤ 5, 5 - l, 0], C) → C'_2
  24. Vector(A, C'_2) → w
  25. Translate(d, w) → d'_2
  26. Dilate(A, If[6 < l ≤ 7, 7 - l, 0], C) → C'_3
  27. Vector(A, C'_3) → m
  28. Translate(d, m) → d'_3
  29. Rotate(d'_2, If[5 < l ≤ 6, ((-(l - 5)) * π / 2), ((-π)) / 2], C) → q
  30. Rotate(d'_3, If[7 < l ≤ 8, (((l - 7) * 4) * π / 3), (4 * π / 3)], C) → r
  31. Dilate(A, If[8 < l ≤ 9, 9 - l, 0], C) → C'_4
  32. Vector(A, C'_4) → n
  33. Translate(d, n) → d'_4
  34. Rotate(d'_4, If[9 < l ≤ 10, (((l - 9) * 7) * π / 6), (7 * π / 6)], C) → s
  35. Midpoint(B, A) → F
  36. Dilate(B, If[10 < l ≤ 11, 11 - l, 0], C) → A'
  37. Segment(B, A') → t
  38. Rotate(B, If[11 < l ≤ 12, ((l - 11) * π / 3), π / 3], B) → A'_1
  39. Rotate(A', If[11 < l ≤ 12, ((l - 11) * π / 3), π / 3], B) → A''
  40. Segment(A'_1, A'') → t'
  41. Dilate(B, If[12 < l ≤ 13, 13 - l, 0], F) → A'_2
  42. Vector(B, A'_2) → u_1
  43. Translate(B, u_1) → A'_3
  44. Translate(A', u_1) → A''_1
  45. Segment(A'_3, A''_1) → t'_1
  46. Rotate(A'_3, If[13 < l ≤ 14, ((l - 13) * π / 3), π / 3], F) → G
  47. Rotate(A''_1, If[13 < l ≤ 14, ((l - 13) * π / 3), π / 3], F) → H
  48. Segment(G, H) → f_1