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Law of Cosines: Open Middle Problem

Law of Cosines: Open Middle Problem
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2020-06-19 00:09
TriangleTrigonometry
This example demonstrates solving an open middle problem using the Law of Cosines. Key mathematical concepts include trigonometry and geometry. Using GeoGebra commands like Circle, Intersect, Textfield, etc., a triangle can be constructed and its properties explored. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Circle(A, a + i + h + g) → d_1
  2. Circle((a + b + c + d, 0), d + e + f + g) → c_1
  3. Intersect(c_1, d_1, 2) → G
  4. Textfield(a) → InputBox1
  5. Textfield(b) → InputBox2
  6. Textfield(c) → InputBox3
  7. Textfield(d) → InputBox4
  8. Textfield(e) → InputBox5
  9. Textfield(f) → InputBox6
  10. Textfield(g) → InputBox7
  11. Textfield(h) → InputBox8
  12. Textfield(i) → InputBox9
  13. Sequence(Circle[((3 * i), 0, 0), 1, xOyPlane], i, 0, 3, 1) → l1, {X = (0, 0, 0) + (cos(t), sin(t), 0), X = (3, 0, 0) + (cos(t), sin(t), 0), X = (6, 0, 0) + (cos(t), sin(t), 0), X = (9, 0, 0) + (cos(t), sin(t), 0)}
  14. Sequence(Segment[((3 * i) + 1, 0), ((3 * i) + 2, 0)], i, 0, 2) → l2, {1, 1, 1}
  15. Rotate(l2, π / 3, (0, 0)) → l2'
  16. Rotate(l2, ((-π)) / 3, (9, 0)) → l2'_1
  17. Rotate(Element[l1, 2], π / 3, (0, 0)) → k
  18. Rotate(Element[l1, 3], π / 3, (0, 0)) → p
  19. Rotate(Element[l1, 4], π / 3, (0, 0)) → q
  20. Rotate(Element[l1, 2], ((-π)) / 3, (9, 0)) → r
  21. Rotate(Element[l1, 3], ((-π)) / 3, (9, 0)) → s
  22. Circle(A, a + b + c + d) → t
  23. Intersect(t, c_1, 1) → F
  24. Polygon(A, E, G) → t1, n, f_1, g_1
  25. Segment(A, E) → j
  26. Mode(l3) → l4
  27. Segment(E, G) → l
  28. Segment(G, A) → m
  29. InteriorAngles(t1) → α, β, γ