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The Law of Cosines

The Law of Cosines. The Law of Cosines. + c 2. - 2 bc cos A. b 2. a 2 = . + c 2. a 2. b 2 = . - 2 ac cos B. - 2 ab cos C. + b 2. a 2. c 2 = . Applying the Law of Cosines. b 2 = a 2 + c 2 - 2 ac cos B = ( 230 ) 2 + ( 150 ) 2 - 2( 230 )( 150 )cos 43 0

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The Law of Cosines

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  1. The Law of Cosines

  2. The Law of Cosines + c2 - 2bc cos A b2 a2 = + c2 a2 b2 = - 2ac cos B - 2ab cos C + b2 a2 c2 =

  3. Applying the Law of Cosines b2 = a2 + c2 - 2ac cos B = (230)2 + (150)2 - 2(230)(150)cos 430 = 24936.59 b = 157.9 m a2 = b2 + c2 - 2bc cos A = (61)2 + (43)2 - 2(61)(43)cos 380 = 1435.09 a = 37.9 cm

  4. Finding an Angle Using the Law of Cosines Find the measure of angle A. a2 = b2 + c2 - 2bc cos A 2bc cos A = b2 + c2 - a2 Using the calculator: Set angle mode to degrees and enter (612 + 432 - 382) ÷ (2 x 61 x 43) = Then press: [COS-1] [ANS] [ )] [ENTER]

  5. Finding an Angle Using the Law of Cosines Given triangle DEF, find . e2 = d2 + f2 - 2df cos E

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