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Trigonometric Functions in Right Triangles by blanchal

Trigonometric Functions in Right Triangles by blanchal
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2017-02-20 04:41
TriangleAngleFunctionTrigonometryGeometric Construction
This example demonstrates how to define and apply trigonometric functions (sine, cosine, tangent) in right triangles. It involves core math concepts like trigonometric definitions, right triangle properties, angle measurement, and side length relationships. GeoGebra commands/objects used include Segment, LineBisector, Point, Intersect, Angle, Line, OrthogonalLine, Polygon, and Distance. Suitable for high school students learning the geometric meaning of trigonometric functions and geometric construction lessons.

GeoGebra Commands & Parameters

  1. Segment(A, B_1) → f
  2. LineBisector(A, B_1) → g
  3. Point(g) → B
  4. Intersect(f, g) → C
  5. Angle(A, C, B) → α
  6. Segment(A, C) → b
  7. Segment(B, A) → c_3
  8. Segment(C, B) → a_4
  9. Line(A, B) → k
  10. Point(k) → D
  11. OrthogonalLine(D, f) → l
  12. Intersect(l, f) → E
  13. Intersect(k, l) → G
  14. Segment(B, D) → e
  15. Segment(D, E) → a'
  16. Segment(E, C) → d
  17. Segment(B, D) → q
  18. Segment(D, E) → r
  19. Segment(E, A) → s
  20. Segment(A, D) → t
  21. Segment(B, C) → a_3
  22. Polygon(A, B, C) → poly1, d_1, a_1, c_1
  23. Polygon(A, D, E) → poly2, f_1, a_2, e_1
  24. Angle(A, E, D) → β
  25. Angle(B, A, C) → γ
  26. Angle(A, B, C) → δ
  27. Angle(A, D, E) → ε
  28. Segment(A, C) → b_2
  29. Segment(A, B) → c_2
  30. Segment(A, B) → c
  31. Distance(A, C) → distanceAC
  32. Distance(A, E) → distanceAE
  33. Distance(A, B) → distanceAB
  34. Distance(A, D) → distanceAD
  35. Distance(C, B) → distanceCB
  36. Distance(E, D) → distanceED