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Law of Cosines

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The Law of Cosines provides a crucial relationship between the angles and sides of a triangle, extending the Pythagorean theorem. Introduced in 1895 by George Albert Wentworth, it allows for various applications, including finding the length of unknown sides and calculating areas. The law can be expressed in three equivalent forms, enabling users to select the most convenient for their calculations. This chapter includes examples with three sides and two sides with one angle, practical homework problems, and an exit slip to demonstrate understanding of when to use the law of sines versus the law of cosines.

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Law of Cosines

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  1. Law of Cosines Chapter 5, Section 6

  2. What is the law of cosines? • Used to provide a relationship between the angles and sides of a triangle • Relates to the pythagorean theorem • First appeared in 1895 in a book by George Albert Wentworth

  3. Law of Cosines Triangle

  4. Examples – 3 sides

  5. Examples – 2 sides, 1 angle

  6. Area of a Triangle • These are 3 equivalent representations • Only need to use one to find the area

  7. Examples – find the area

  8. Homework • page 494 #3-18 multiples of 3 • Exit Slip: Explain how you know to use the law of sines or the law of cosines in a problem.

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