MathPlotAI Logo MathPlotAI

Law of Cosines by aarong

Law of Cosines by aarong
Loading the math board and drawing, please wait…
2016-01-24 07:19
VectorTrigonometryGeometric Construction
This example illustrates the Law of Cosines, which states that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice their product with the cosine of the included angle. Key concepts include trigonometry and vectors. Using GeoGebra commands such as Line, OrthogonalLine, Intersect, Vector, Angle, and Segment, the geometric meaning of the Law of Cosines is vividly demonstrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → AB
  2. OrthogonalLine(C, AB) → CD
  3. Intersect(AB, CD) → D
  4. Vector(A, B) → a
  5. Vector(A, C) → b
  6. Vector(C, B) → u
  7. Angle(B, D, C) → α
  8. Angle(B, A, C) → θ
  9. Segment(D, C) → c
  10. Segment(D, B) → d
  11. Angle(C, D, B) → β
  12. Angle(C, A, B) → γ