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Law of Sines: How Many Triangles?

Law of Sines: How Many Triangles?
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2017-01-14 04:33
TriangleTrigonometryGeometric Construction
This example illustrates the different cases of the Law of Sines — no triangle, right triangle, one triangle, and the ambiguous case. Using GeoGebra commands such as Segment, Angle, Intersect, Circle, etc., it demonstrates how to determine the number of triangles based on given conditions. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment((0, 0), (10, 0)) → base
  2. Segment((0, 0), (3, 2)) → a
  3. Angle(base, a) → α
  4. Segment((3, 2), (3, 0)) → hseg
  5. Intersect(a, hseg) → A
  6. Intersect(base, hseg) → B
  7. Circle(A, B) → c
  8. Circle(A, C) → d
  9. Circle(A, D) → e
  10. Circle(A, E) → f
  11. Point(d) → F
  12. Segment(A, F) → a_1
  13. Point(c) → G
  14. Segment(A, G) → b_1
  15. Point(e) → H
  16. Segment(A, H) → g
  17. Point(f) → I
  18. Segment(A, I) → b