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Law of Cosines

Law of Cosines. Geometry Honors. Remark:. We only used the Law of Sines to solve Case 1 (SAA or ASA) and Case 2 (SSA) of an oblique triangle. We will now solve: Case 3 – Two sides and the included angle (SAS) Case 4 – Three sides (SSS). More Remarks.

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Law of Cosines

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  1. Law of Cosines Geometry Honors

  2. Remark: • We only used the Law of Sines to solve Case 1 (SAA or ASA) and Case 2 (SSA) of an oblique triangle. • We will now solve: • Case 3 – Two sides and the included angle (SAS) • Case 4 – Three sides (SSS)

  3. More Remarks • The Law of Sines does not work in either of these cases. • To use the Law of Sines we must know at least one side and its opposite angle. If we are given three sides (SSS), or two sides and their included angle (SAS), none of the ratios would be complete. • We rely on the Law of Cosines.

  4. Law of Cosines

  5. In Greek

  6. Note

  7. Solve SAS Triangle

  8. Solve SSS Triangle

  9. Heron’s Formula • The Law of Cosines can be used to establish the following formula for the area of a triangle. This formula is credited to the Greek mathematician Heron (c. 100 B.C.)

  10. Heron’s Area Formula

  11. Example • Find the area of the triangular region having sides of lengths a = 47 yards, b = 58 yards, and c = 78.6 yards.

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