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Law of Cosines

Law of Cosines. Section 5.6 . Law of Cosines. We know that we can use the Law of Sines to solve a triangle in the A-A-S and S-S-A cases, but what about the S-A-S case, where we don’t have an angle and it’s opposite side length?.

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Law of Cosines

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  1. Law of Cosines Section 5.6

  2. Law of Cosines We know that we can use the Law of Sines to solve a triangle in the A-A-S and S-S-A cases, but what about the S-A-S case, where we don’t have an angle and it’s opposite side length? The length of “a” and the angles B and C seem to be “pre-determined” by the scenario, right? Well they are. We should be able to solve for those missing values… But how?

  3. Here’s how… position the triangle such that A is at the origin and B is on the x-axis. We need to solve for “a” in terms of b, c, and A. Solve for “a” using the distance formula. The last line is one version of the Law of Cosines which enables one to solve a triangle given S-A-S. You can also use this for the S-S-S scenario. Thus it is no longer necessary to have an angle and its opposite side.

  4. Law of Cosines

  5. Two More Fun Formulas Area of Triangle when given S-A-S Area of Triangle when given S-S-S

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