Law of Cosines

Ariana and Brittany

In any triangle, given two sides & the included angle, the third side is given by the COSINE FORMULA

Formula: c^2 = A^2 + B^2 - 2abCOS(c)


Example:

step 1 start with formula

c^2 = A^2 + B^2 - 2abCOS(c)

step 2 insert values for A, B, & C

c^2 = 236^2 + 8.2^2 - 2 x 23.6 x 8 x cos (60dg)

step 3 evaluate right side

c^2 = 430.6

step 4 square root both sides

c = 20.8


If a problem refers to three sides and one angle, use LAW OF COSINES

Formula: C^2 = a^2 + b^2 - 2ab cosC



Example:

step 1 original formula

a^2 = b^2 + c^2 - 2bc cosA

step 2 insert values

a^2 = 12^2 + 20^2 - 2 x 12 x 20 cos (40dg)

step 3 evaluate

a^2 = 176.29888

step 4 take the square root of each side

a = 13.2777 ~ 13