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Law of Cosines

Law of Cosines. No longer dealing with Right Triangles!. Law of cosines is a tool to solve triangles that are not right-angled (oblique triangles) We need to know three things in order to use the law: Either all 3 sides , or two sides of a triangle and their included angle. If we know:

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Law of Cosines

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  1. Law of Cosines

  2. No longer dealing with Right Triangles! • Law of cosines is a tool to solve triangles that are not right-angled (oblique triangles) • We need to know three things in order to use the law: Either all 3 sides, or two sides of a triangle and their included angle

  3. If we know: a, b, and θ We can find side c. c a θ b

  4. The Law of Cosines • For any • Notice the side on the left of the = sign is the same as the angle you are taking cos of.

  5. Example 1 • Use the Law of Cosines to find side length a.

  6. Example 1 Cont… Since we are given the angle A, and we are looking for side a, we will use original plug in values simplify * a Square root

  7. You try!

  8. Use the law in a different way: • Find angle T.

  9. Solution • 81 = 245 – 196 • – 164 = – 196 • .8367….. = • T = 33.2°

  10. Apply Law to more difficult example: In parallelogram BCDE, angle C is 65°. How long is each diagonal to one decimal place?

  11. Solution CD =6.4 BE = 9.4 Trick: Recall, Angle c and angle E sum to 180, so we can determine angle E = 115°

  12. Homework • Law of Cosines Page 511 • Problems 1,3,7

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