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Trigonometric Ratios in Right Triangle Context

Trigonometric Ratios in Right Triangle Context
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2016-05-01 05:02
TriangleAngleFunctionTrigonometryGeometric Construction
In collections GA Chapter 8: Right Triangles and Trigonometry
This example illustrates the true meanings of the 3 main trigonometric ratios (sine, cosine, tangent) defined in the context of a right triangle. It covers core math concepts like trigonometric definitions and side-angle relationships. The construction uses GeoGebra commands such as Segment, OrthogonalLine, Point, Ray, Angle, Rotate, Polygon, Midpoint, and Vector. Ideal for high school students and teachers learning or teaching trigonometric geometric definitions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → E
  4. Ray(B, E) → c
  5. Angle(A, B, E) → α
  6. Point(c) → C
  7. Segment(C, A) → d
  8. Angle(B, C, A) → β
  9. Segment(B, C) → e
  10. Rotate(B, If[0 < f ≤ 1, (f * β), 0], C) → B'
  11. Rotate(C, If[0 < f ≤ 1, (f * β), 0], C) → C'
  12. Segment(B', C') → e'
  13. Angle(C, A, B) → γ
  14. Rotate(A, If[0 < g ≤ 1, ((-g) * γ), 0], A) → A'
  15. Rotate(B, If[0 < g ≤ 1, ((-g) * γ), 0], A) → B'_1
  16. Segment(A', B'_1) → a'
  17. Rotate(B, If[0 < h ≤ 1, ((-h) * α), 0], B) → B'_2
  18. Rotate(C, If[0 < h ≤ 1, ((-h) * α), 0], B) → C'_1
  19. Segment(B'_2, C'_1) → e'_1
  20. Polygon(B, A, C) → poly1, c_1, b_1, a_1
  21. Midpoint(e') → D
  22. Vector(F, D) → u
  23. Midpoint(a') → G
  24. Vector(H, G) → v
  25. Midpoint(e'_1) → I
  26. Vector(J, I) → w
  27. Ray(B, A) → j