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Three Right-Angled Triangles and Trigonometric Ratios

Three Right-Angled Triangles and Trigonometric Ratios
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2012-06-14 05:24
TriangleTrigonometrySlider Animation
In collections Trig Ratios
This example demonstrates the calculation of trigonometric ratios in three right-angled triangles. Key mathematical concepts include trigonometry, similarity of triangles, and geometric transformations. Construction involves GeoGebra commands such as Intersect, Point, Circle, and Rotate. Suitable for middle or high school mathematics classes to enhance understanding of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Rotate(B, α, A) → B'
  5. Angle(B, A, B') → β
  6. Circle(D, C) → d
  7. Rotate(C, α, D) → C'
  8. Angle(C, D, C') → γ
  9. Circle(G, F) → e
  10. Rotate(F, α, G) → F'
  11. Angle(F, G, F') → δ
  12. Tangent(F, e) → a,
  13. Tangent(C, d) → b,
  14. Tangent(B, c) → f,
  15. Ray(G, F') → g
  16. Ray(D, C') → h
  17. Ray(A, B') → i
  18. Intersect(a, g) → E
  19. Intersect(h, b) → H
  20. Intersect(i, f) → I
  21. Segment(G, F) → j
  22. Segment(G, E) → k
  23. Segment(F, E) → l
  24. Segment(A, B) → m
  25. Segment(B, I) → n
  26. Segment(A, I) → p
  27. Segment(D, C) → q
  28. Segment(C, H) → r
  29. Segment(H, D) → s
  30. Angle(I, B, A) → ε
  31. Angle(H, C, D) → ζ
  32. Angle(E, F, G) → η

AI Drawing Prompt Reference

Please draw three right-angled triangles and calculate their trigonometric ratios. First, draw a circle at the intersection of the coordinate axes, then select a point on this circle and rotate it to get another point, forming the first right-angled triangle. Repeat this process to draw two more right-angled triangles in different positions. Each triangle includes one right angle and two acute angles, and the lines connecting the rotated points with the original points form the sides of the triangles. Finally, calculate the sine, cosine, and tangent values for each angle in the triangles.
The prompt above was compiled from the original drawing commands and is for reference only.