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The Cosine Law: PWW by S. Kung

This is a proof by Sidney H. Kung:

The Cosine Law: PWW by S. Kung

By the Intersecting Chords Theorem,

$(a+c)(a-c)=(2a\cos\theta-b)b,$

i.e., $a^2-c^2=2ab\cos\theta -b^2.$

References

  1. R. B. Nelson, Proofs Without Words, MAA, 1993, p. 32
  • The Law of Cosines (Cosine Rule)
  • The Illustrated Law of Cosines
  • The Law of Sines and Cosines
  • The Law of Cosines: Plane Tessellation
  • The Law of Cosines: after Thâbit ibn Qurra
  • The Law of Cosines: Unfolded Version
  • The Law of Cosines (Independent of the Pythagorean Theorem)
  • The Cosine Law by Similarity
  • The Law of Cosines by Larry Hoehn
  • The Law of Cosines - Another PWW
  • The Law of Cosines - Yet Another PWW
  • Law of Cosines by Ancient Sliding
  • The Cosine Law: PWW by S. Kung

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