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Law of Cosines by Esther Gruenhut

Law of Cosines by Esther Gruenhut
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2017-05-01 15:58
TriangleTrigonometryGeometric 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 trigonometric functions and geometric construction. It uses commands like Rotate, Line, Circle, Intersect, Segment, Point, Polygon, etc., suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Rotate(B, (-γ), C) → B_1
  2. Angle(B_1, C, B) → α
  3. Line(B_1, C) → line_{AC}
  4. Circle(B, C) → d
  5. Line(C, B) → line_{BC}
  6. Intersect(d, line_{BC}, 2) → D
  7. Intersect(d, line_{AC}, 2) → E
  8. Segment(D, B) → seg_{BD}
  9. Segment(E, C) → seg_2
  10. Point(seg_2) → A
  11. Polygon(A, C, B) → poly1, b, a, c
  12. Segment(E, A) → seg_{EA}
  13. Line(A, B) → line_{AB}
  14. Intersect(d, line_{AB}, 1) → F
  15. Intersect(d, line_{AB}, 2) → G
  16. Segment(F, A) → seg_1
  17. Segment(B, G) → seg_{AF}
  18. Segment(D, E) → f
  19. Angle(D, E, C) → β
  20. Segment(E, C) → seg_{EC}