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8.1.3 – Law of Cosines

8.1.3 – Law of Cosines. Recall… The Law of Sines was for two situations; 1) Two angles and a side 2) Two sides and a non-included angle Could NOT be used when we knew 3 sides or two sides and an included angle .

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8.1.3 – Law of Cosines

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  1. 8.1.3 – Law of Cosines

  2. Recall… • The Law of Sines was for two situations; • 1) Two angles and a side • 2) Two sides and a non-included angle • Could NOT be used when we knew 3 sides or two sides and an included angle

  3. As a result, we need another way to help us in the event we know the SSS or SAS (with included angle) situation • Luckily, a property similar to the Pythagorean theorem may be derived

  4. Law of Cosines • Let A, B, and C represent angles • Let a, b, and c represent side lengths

  5. Considered an extension of the Pythagorean theorem • Can be used with right triangles as well

  6. Example. A bullet is fired and ricochets off a metal sign 100 feet away, making an 80 degree angle as it speeds towards a tree, embedding itself in the tree. If the sign and tree are 60 feet apart, how far did the bullet stop from where it was fired?

  7. Example. Determine the three angles for a triangle if a = 3, b = 5, and c = 7 (all in inches).

  8. Example. While driving in a rally, the navigator instructs a driver to travel 11km east. They then turn at 20 degrees, and travel another 15 km to a second stop point. What is the distance between the starting point and the second stop point?

  9. Assignment • Pg. 612 • 43, 47, 51, 55, 59, 62, 63, 67

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