Lesson 6.1- Law of Sines Provided by Vivian Skumpija and Amy Gimpel

When to use the Law of Sines To solve an oblique triangle Given: –T–Two angles and any side (AAS or ASA) –T–Two sides and an angle opposite one of them (SSA or ASS) ***Always remember to keep your calculator in degree mode ***

AAS If C=102.3 °, B=28.7°, b=27.4 A= ° Since you have an angle measurement and its opposite side you can set up the equation… a= c=57.75 NOTE: To solve for c, you always go back to your original equation to avoid using rounded values.

ASS (Single Solution) If b= 795.1, c=775.6, B= 51.85° Since side b is greater than the other given side, there is only one solution ° B A C ° ° NOTE: To solve for sin c, you must use the answer with inverse sine (on calculator: 2 nd Sin, 2 nd ANS)

ASS (No Solution) a=7, b=15, A=98° This triangle can not be solved for any answers, which would make it NO SOLUTION.

a’=10 B’ A’ 52© © 25.7 © b’=5.5 c’=12.4 ASS (Two Solutions) First: solve for the regular triangle A B C 52 © a=10c=12.4 b=9.8 C’ 77.7 © © Because the side across from the given angle is smaller than the other side, there is another set of solutions…

Finding the Area Since sides a and b are given and so is angle C… 102° a=90 b=52

Lesson 6.2- Law of Cosines

When to use the Law of Cosines To solve an oblique triangle Given: –T–Three sides (SSS) –T–Two sides and their included angle (SAS) ***Always remember to keep your calculator in degree mode ***

a=3, b=5, c=7 pick the largest solve for the rest of the triangle SSS

SAS a=4.2, c=7.5, B=32° Because you have angle B, you want to solve for side b… …Then you solve for the rest using the Law of Sines

Heron’s Area Formula If a=43m, b=53 m, c=72 m Substitute for S

THAT’S ALL THERE IS TO IT