Xavier Noel Albrecht
Salena Lemieux
Introduction
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
Example #2-Finding a side
 a² = b² + c² −2(b)(c)cos(A°)
 a² = 52² + 16² −2(52)(16)cos(115°)
 a² = 2,704 + 256 − 1,664cos(115°)
 a² = 2,960− 1,664(-.423)
 a² = 2,960 +703
 a² = 3663
 a=36631/2
 a=60.5
Example #3 Finding an angle
 a² = b² + c² −2(a)(b)cos(A°)
 14² = 20 ² + 12² −2(12)(20)cos(A°)
 14²- 20 ² - 12² = (12)(20)cos(A°)
 -348=-480cos(A°)
 0.675=cos(A°)
 cos-1(0.25)
 Cos(A°)=47.5°
Example #4- Finding an angle
 a² = b² + c² −2(a)(b)cos(A°)
 25² = 32² + 37² −2(32)(37)cos(A°)
 625 = 2393 − 2,368 cos(A°)
 -1760=-2,368cos(A°)
 0.7432=cos(A°)
 cos-1(0.7432)
 Cos(A°)=42°
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-ofcosines-flash-cards/
 Notes from class
 Problems from book