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Law of Sines by Andrea Guerra

Law of Sines by Andrea Guerra
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2015-03-10 11:43
TrigonometryGeometric ConstructionSlider Animation
This applet dynamically demonstrates the relationship between side lengths and angles in the Law of Sines, especially the ambiguous case. Key mathematical concepts include trigonometry and geometric construction. It utilizes commands such as Circle, Intersect, Segment, Rotate, Angle, Ray, and Polygon in GeoGebra. Suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Circle(A, c_1) → d
  2. Intersect(d, b_3, 2) → B
  3. Segment(A, B) → c
  4. Circle(B, a_3) → f
  5. Rotate(B, α_1, A) → B'
  6. Angle(B, A, B') → α
  7. Ray(A, B') → b
  8. Intersect(f, b, 1) → C_1
  9. Intersect(f, b, 2) → C_2
  10. Segment(C_1, B) → a_1
  11. Segment(C_2, B) → a_2
  12. Segment(C_1, A) → b_1
  13. Segment(A, C_2) → b_2
  14. Polygon(A, B, C_1) → poly1, c_2, a, b_4
  15. Polygon(A, B, C_2) → poly2, c_3, a_4, b_5
  16. Angle(C_1, B, A) → β
  17. Angle(A, C_1, B) → γ
  18. Angle(A, C_2, B) → γ_2
  19. Angle(C_2, B, A) → β_2

AI Drawing Prompt Reference

Draw a dynamic illustration showing the relationship between side lengths and angles in a triangle, including two triangles and a slider to demonstrate the Law of Sines, especially the ambiguous case. Start by drawing a circle, find intersections, draw segments and rays, then draw another circle and rotate it to get new points and angles, finally connect the points to form polygons and label the angles and sides to show the application of the Law of Sines.
The prompt above was compiled from the original drawing commands and is for reference only.