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Formula for Finding Angle between Two Planes

Formula for Finding Angle between Two Planes
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2019-01-05 15:59
AngleTrigonometrySolid Geometry
This example demonstrates how to use a formula to find the angle between two planes. Key mathematical concepts include plane geometry and trigonometry. Using GeoGebra commands such as Rotate, Ray, Point, and Angle, the intersection angle of two planes is visually demonstrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Rotate((1, 0), ((-β)) / 2) → A_2
  2. Rotate(A_2, (-γ)) → P_2
  3. Ray(O, A_2) → g
  4. Point(g) → B
  5. Rotate((1, 0), β / 2) → A_1
  6. Ray(O, A_1) → f
  7. Point(f) → A
  8. Rotate(A_1, α) → P_1
  9. Angle(A_2, O, A_1) → δ
  10. OrthogonalLine(P_1, f) → j
  11. OrthogonalLine(P_2, g) → k
  12. Intersect(j, k) → F
  13. Intersect(j, f) → C
  14. Intersect(k, g) → D
  15. Segment(P_1, C) → l
  16. Segment(C, F) → m
  17. Segment(F, D) → n
  18. Segment(D, P_2) → p
  19. Segment(O, P_1) → h
  20. Segment(O, P_2) → i
  21. Segment(O, C) → q
  22. Segment(O, D) → r
  23. Rotate(P_1, (t * (180° - diheral)), f) → D'
  24. Rotate(P_2, ((-t) * (180° - diheral2)), r) → D''
  25. Polygon(O, D', A) → t1, a, b, c
  26. Polygon(D'', O, B) → t2, g_1, q_1, r_1
  27. Polygon(P_1, O, A) → t3, d, f_1, m_1
  28. Polygon(O, B, P_2) → t4, e, n_1, p_1
  29. Segment(D', F) → s
  30. Angle(C, O, P_1) → ε
  31. Angle(P_2, O, D) → ζ
  32. Angle(D, O, D'') → η
  33. Angle(C, O, D') → θ
  34. Angle(F, C, D') → ι
  35. Segment(P_1, A) → h_1
  36. Segment(P_2, B) → i_1
  37. Segment(C, A) → j_1
  38. Segment(D, B) → k_1
  39. Segment(A, B) → l_1
  40. Segment(D'', D) → s_1
  41. Segment(D', C) → t_1
  42. Polygon(O, A, B) → t5, c_1, a_1, b_1
  43. Angle(P_1, C, O) → κ
  44. Angle(O, D, P_2) → λ
  45. Angle(D'', D, O) → μ
  46. Angle(D', C, O) → ν