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Sine Rule - Ambiguous Case Worksheet

Sine Rule - Ambiguous Case Worksheet
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2017-08-07 17:52
TriangleTrigonometryGeometric Construction
This example demonstrates the ambiguous case of the sine rule in triangle construction, where given two angles and one side or two sides and one angle might lead to two different triangles. It involves core concepts like the sine rule, triangle solving, and geometric construction. GeoGebra commands used include Polygon, Circle, Line, Intersect, Segment, and Angle. Suitable for high school mathematics teaching or student exploration of triangle solving complexity.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Polygon(D, E, F) → poly2, f, d, e
  3. Polygon(G, H, I) → poly3, i, g, h
  4. Polygon(K, L, M) → poly4, m, k, l
  5. Polygon(N, O, P) → poly5, p, n, o
  6. Polygon(Q, R, S) → poly6, s, q, r
  7. Circle(B, C) → t
  8. Line(A, C) → f_1
  9. Intersect(t, f_1, 2) → T
  10. Segment(B, T) → g_1
  11. Circle(E, F) → c_1
  12. Line(D, F) → h_1
  13. Intersect(c_1, h_1, 2) → U
  14. Segment(D, U) → i_1
  15. Segment(U, E) → j_1
  16. Circle(R, S) → d_1
  17. Line(Q, S) → k_1
  18. Intersect(d_1, k_1, 2) → V
  19. Segment(V, R) → l_1
  20. Segment(V, S) → m_1
  21. Circle(O, N) → e_1
  22. Intersect(e_1, o, 2) → W
  23. Segment(O, W) → n_1
  24. Circle(L, K) → p_1
  25. Intersect(p_1, h_1, 2) → Z
  26. Segment(L, Z) → q_1
  27. Circle(I, H) → r_1
  28. Intersect(r_1, i, 2) → J
  29. Segment(I, J) → j
  30. Segment(C, T) → s_1
  31. Angle(B, C, A) → α
  32. Angle(B, T, A) → β
  33. Angle(C, A, B) → γ
  34. Angle(E, U, D) → δ
  35. Angle(E, F, D) → ε
  36. Angle(F, D, E) → ζ
  37. Angle(R, V, Q) → η
  38. Angle(R, S, Q) → θ
  39. Angle(S, Q, R) → ι
  40. Angle(I, G, H) → κ
  41. Angle(G, J, I) → λ
  42. Angle(G, H, I) → μ
  43. Angle(L, M, K) → ν
  44. Angle(M, Z, L) → ξ
  45. Angle(M, K, L) → ο
  46. Angle(O, P, N) → ρ
  47. Angle(P, W, O) → σ
  48. Angle(P, N, O) → τ

AI Drawing Prompt Reference

Draw two triangles, one constructed by given two sides and an angle, and the other by given two angles and a side, to demonstrate the ambiguous case of the sine rule. Start by drawing the sides and vertices of the triangles, then use circles and lines to construct possible intersection points, connecting these points to form two different triangles. Finally, label the interior angles of each triangle to show the angle relationships.
The prompt above was compiled from the original drawing commands and is for reference only.