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Cosine Rule Construction

Cosine Rule Construction
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2015-04-01 16:51
TriangleTrigonometryGeometric Construction
This example uses the Cosine rule to calculate the missing angle and length in a triangle. It demonstrates how to use GeoGebra commands such as Polygon, Angle, Midpoint, and Segment for geometric construction. Suitable for students in middle school and above learning trigonometry and geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Angle(B, A, C) → α
  3. Angle(A, C, B) → β
  4. Angle(C, B, A) → γ
  5. Angle(B, A, C) → δ
  6. Midpoint(a) → D
  7. Midpoint(b) → E
  8. Midpoint(c) → F
  9. Segment(B, A) → f
  10. Segment(A, C) → g
  11. Segment(C, B) → h
  12. Angle(A, C, B) → ε
  13. Angle(C, B, A) → ζ

AI Drawing Prompt Reference

Draw a triangle with labeled vertices and angles. Calculate and mark a missing angle and side length using the cosine rule. Start by drawing the triangle's sides, then label the angles at each vertex. Find and mark the midpoints of each side, connect the vertices to these midpoints, and finally calculate the missing angle and side length, labeling the results accordingly.
The prompt above was compiled from the original drawing commands and is for reference only.