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Right Triangle Ratios by Jessica Driver

Right Triangle Ratios by Jessica Driver
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2017-11-29 00:46
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the ratio relationships between side lengths and angles in a right triangle. Key math concepts include trigonometric functions, Pythagorean theorem, and angle measurement. GeoGebra commands used in construction are Rotate, Angle, Ray, OrthogonalLine, Intersect, Segment, and Polygon. Suitable for high school mathematics education to help students understand the fundamental properties and ratio relationships of right triangles.

GeoGebra Commands & Parameters

  1. Rotate(C, (-B), B_{4}) → A'
  2. Angle(A', B_{4}, C) → β
  3. Ray(B_{4}, C) → f
  4. Ray(B_{4}, A') → g
  5. OrthogonalLine(C, f) → h
  6. Intersect(h, g) → A
  7. Segment(C, A) → b
  8. Segment(A, B_{4}) → c
  9. Segment(B_{4}, C) → a
  10. Rotate(C_1, (-B), B_1) → A'_1
  11. Angle(A'_1, B_1, C_1) → β_1
  12. Ray(B_1, C_1) → f_1
  13. Ray(B_1, A'_1) → g_1
  14. OrthogonalLine(C_1, f_1) → h_1
  15. Intersect(h_1, g_1) → A_1
  16. Segment(C_1, A_1) → b_1
  17. Segment(A_1, B_1) → c_1
  18. Segment(B_1, C_1) → a_1
  19. Rotate(C_2, (-B), B_2) → A'_2
  20. Angle(A'_2, B_2, C_2) → β_2
  21. Ray(B_2, C_2) → f_2
  22. Ray(B_2, A'_2) → g_2
  23. OrthogonalLine(C_2, f_2) → h_2
  24. Intersect(h_2, g_2) → A_2
  25. Segment(C_2, A_2) → b_2
  26. Segment(A_2, B_2) → c_2
  27. Segment(B_2, C_2) → a_2
  28. Rotate(C_3, (-B), B_3) → A'_3
  29. Angle(A'_3, B_3, C_3) → β_3
  30. Ray(B_3, C_3) → f_3
  31. Ray(B_3, A'_3) → g_3
  32. OrthogonalLine(C_3, f_3) → h_3
  33. Intersect(h_3, g_3) → A_3
  34. Segment(C_3, A_3) → b_3
  35. Segment(A_3, B_3) → c_3
  36. Segment(B_3, C_3) → a_3
  37. Polygon(J_1, K_1, L_1, M_1) → poly1_1, j_4, k_1, l_1, m_1