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Trigonometry SOHCAHTOA: Dynamic Right Triangle Ratios

Trigonometry SOHCAHTOA: Dynamic Right Triangle Ratios
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2020-03-09 09:10
TriangleAngleTrigonometryTransformationSlider Animation
In collections Strand 2: Geometry and Trigonometry
① This GeoGebra example dynamically demonstrates the sine, cosine, and tangent (SOHCAHTOA) relationships in a right triangle, showing how the ratios of opposite, adjacent, and hypotenuse sides change with the angle. ② Core mathematical concepts include trigonometric definitions, right-triangle side ratios, similar triangles, and the correspondence between angles and function values. ③ Construction highlights: using Segment, OrthogonalLine, Point, Angle, Polygon, Vector, Translate, and Dilate commands to build the right triangle and generate multiple similar copies, with sliders or dynamic points adjusting angle α and updating side labels (OPPOSITE, ADJACENT, HYPOTENUSE) and function values in real time. ④ Suitable for middle-to-high school students learning basic trigonometry, and useful for classroom demonstrations or self-paced exploration.

GeoGebra Commands & Parameters

  1. Segment(A, B_1) → ADJACENT_A
  2. OrthogonalLine(B_1, ADJACENT_A) → b
  3. Point(b) → B
  4. Segment(A, B) → HYPOTENUSE_1
  5. Segment(B, B_1) → OPPOSITE_A
  6. Angle(B, B_1, A) → α
  7. Polygon(A, B_1, B) → poly1, c, a, b_1
  8. Vector(D, E) → u
  9. Vector(F, G) → v
  10. Translate(A, v) → A'_3
  11. Translate(B_1, v) → B'_3
  12. Translate(B, v) → C'
  13. Polygon(A'_3, B'_3, C') → poly1', c', a', b'
  14. Translate(A, v) → A'_1
  15. Translate(B_1, v) → B'_1
  16. Segment(A'_1, B'_1) → ADJACENT'
  17. Translate(A, v) → A'_2
  18. Translate(B, v) → C'_1
  19. Segment(A'_2, C'_1) → HYPOTENUSE'
  20. Translate(B, v) → C'_2
  21. Translate(B_1, v) → B'_2
  22. Segment(C'_2, B'_2) → OPPOSITE'
  23. Translate(D, v) → D'
  24. Dilate(A'_3, 0.5, H) → A'
  25. Dilate(B'_3, 0.5, H) → B''
  26. Dilate(C', 0.5, H) → B'
  27. Polygon(A', B'', B') → poly1'', c'', a'', b''
  28. Dilate(A'_1, 0.5, H) → I
  29. Dilate(B'_1, 0.5, H) → J
  30. Segment(I, J) → ADJACENT_A'
  31. Dilate(A'_2, 0.5, H) → K
  32. Dilate(C'_1, 0.5, H) → L
  33. Segment(K, L) → HYPOTENUSE
  34. Dilate(C'_2, 0.5, H) → M
  35. Dilate(B'_2, 0.5, H) → N
  36. Segment(M, N) → OPPOSITE_A'
  37. Angle(B_1, A, B) → β
  38. Angle(b'', OPPOSITE_A') → δ
  39. Angle(A, B, B_1) → ε
  40. Angle(B', B'', A') → ζ
  41. Segment(A', B'') → OPPOSITE_B'
  42. Segment(B'', B') → ADJACENT_B'
  43. Segment(A, B_1) → OPPOSITE_B
  44. Segment(B_1, B) → ADJACENT_B
  45. Angle(B'', A', B') → η