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The Law of Cosines

The Law of Cosines. Lesson 5.2. Theorem. Law of Cosines: In any triangle ABC, c 2 = a 2 +b 2 -2ab cosC a 2 = b 2 + c 2 -2bc cos A b 2 = a 2 + c 2 -2ac cos B. Example 1.

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The Law of Cosines

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  1. The Law of Cosines Lesson 5.2

  2. Theorem • Law of Cosines: In any triangle ABC, c2 = a2+b2-2ab cosC a2 = b2 + c2 -2bc cos A b2 = a2 + c2 -2ac cos B

  3. Example 1 • To the nearest degree, find the measure of the smallest angle in a triangle whose sides have lengths 4 cm, 5 cm , and 6 cm. c2 = a2+b2-2ab cosC 42 = 52+62-2*5*6 cosC 4 cm 5 cm 16 = 25+36-60 cosC 6 cm x 16 = 25+36-60 cosC .75 = cosC -45= -60 cosC C = 41.41

  4. Example 2 • A parallelogram has a 70° angle and sides of length 10 in. and 15 in. What is the length of its longer diagonal? c2 = a2+b2-2ab cosC c2 = 102 + 152 - 2(10)(15)cos(110) c2 = 100 + 225 – 300*(-.342) c2 = 427.61 c = 20.68 15 70 110 10 10 110 70 15

  5. Homework pages 318 – 319 2 – 7 11 - 12

  6. Discovery Ed. • http://player.discoveryeducation.com/index.cfm?guidAssetId=A691574C-39AB-4E4A-9B27-7643422C3F6B&blnFromSearch=1&productcode=US

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