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Angle Between Planes

Angle Between Planes
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2019-01-30 08:54
VectorSolid GeometryGeometric Construction
This example demonstrates how to calculate the angle between two planes using vector dot product, normal vectors, and the cosine theorem. It involves constructing segments, circles, points, angles, vectors, polygons, and rays with GeoGebra commands like Segment, Circle, Point, Angle, Vector, Polygon, Ray, Intersect. Suitable for high school solid geometry teaching and geometric construction practice.

GeoGebra Commands & Parameters

  1. Segment(rotateLRc, rotateLR0) → a
  2. Circle(rotateLRc, rotateLR0) → c
  3. Point(c) → rotateLR
  4. Angle(rotateLR0, rotateLRc, rotateLR) → α
  5. Segment(rotateLRc, rotateLR) → b
  6. Circle(rotateUDc, rotateUD0) → d
  7. Point(d) → rotateUD
  8. Angle(rotateUD0, rotateUDc, rotateUD) → β
  9. Segment(rotateUDc, rotateUD0) → e
  10. Segment(rotateUDc, rotateUD) → f
  11. Vector(O, O + (0, sin(β))) → Oz
  12. Vector(O, O + (cos(α), (sin(α) * cos(β)))) → Ox
  13. Vector(O, O + ((-1 * sin(α)), (cos(α) * cos(β)))) → Oy
  14. Polygon(A1, A3, A4, A6) → poly1, a1, a3, a4, a6
  15. Polygon(A10, A12, A13, A15) → poly2, a10, a12, a13, a15
  16. Angle(A14, P, A2) → θ_1
  17. Ray(P, A14) → i
  18. Ray(P, A2) → j
  19. Point(j) → C
  20. Point(i) → R
  21. Circle(P, 4) → k
  22. Intersect(k, j, 1) → Q
  23. Segment(A, B) → l
  24. Segment(A16, A18) → m
  25. Segment(A18, A17) → n
  26. Segment(A19, A21) → p
  27. Segment(A21, A20) → q