5.6 Law of Cosines. Xavier Noel Albrecht Salena Lemieux. Introduction. Explanation. Law of Cosine— a 2 =b 2 +c 2 -2bcCosA b 2 =a 2 +c 2 -2acCosB c 2 =a 2 +b 2 -2abCosC. Explanation. First you need to identify what you have
Explanation Law of Cosine— a2=b2+c2-2bcCosA b2=a2+c2-2acCosB c2=a2+b2-2abCosC
Explanation First you need to identify what you have You need to have three sides (SSS) OR two sides and an angle in between them (SAS) Put the information that you have and put it into the correct formula Solve for the missing side or angle
Example #1- Finding a side a² = b² + c² −2(a)(b)cos(A°) a² = 20² + 13² −2(20)(13)cos(66°) a² = 400 + 169 −520cos(66°) a² = 569 −211 a² = 358 a = 3581/2 a = 18.9
Checking The longest side has the largest angle and the smallest side has the smallest angle This won’t give you the exact answer but it will help see if you have the right idea
Activity http://quizlet.com/16377121/law-of-sines-and-law-of-cosines-flash-cards/ Who ever can get the most right wins
Assessment a=12 b=21 C=95° Find side c. A)23.261 B)30 C)162.32 a=3 b=7 c=6 Find angle B° A)126.83° B)90° C)83.621° c=8 B=131 a=13 Find side b A)53 B)9.825 C)528.9 a=27 b=19 c=24 Find angle A° A)70° B)76.817° C)71.867° A=55° b=12 c=7 Find side a A)3.83 B)15 C)9.831 A=55° b=14 c=23 Find side a A)18.858 B)20 C)16.252 C=42° b=12 a=14 Find side c A)9.503 B)15 C)30.59 A=82° b=22 c=31 Find side a A)40 B)82.453 C)35.428 C=65° a=19 b=22 Find side c A)50 B)22.174 C)47.122 B=31° a=8 c=11 Find side b A)5.843 B)3.485 C)12
Work Cited http://www.mathwarehouse.com/trigonometry/law-of-cosines-formula-examples.php http://quizlet.com/16377121/law-of-sines-and-law-of-cosines-flash-cards/ Notes from class Problems from book