# 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