# How do you use the law of cosines if you are given x = 12.37, y=10, z=15?

Jun 5, 2015

By the Law of Cosines:
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} = {y}^{2} + {z}^{2} - 2 y z C o s \left(X\right)$
$\textcolor{w h i t e}{\text{XXXX}}$or
$\textcolor{w h i t e}{\text{XXXX}}$$C o s \left(X\right) = \frac{{y}^{2} + {z}^{2} - {x}^{2}}{2 y z}$

Therefore
$\textcolor{w h i t e}{\text{XXXX}}$$X = A r \mathcal{o} s \left(\frac{{y}^{2} + {z}^{2} - {x}^{2}}{2 y z}\right)$

Plugging the given values for $x , y , \mathmr{and} z$ we can calculate the angles $X , Y , \mathmr{and} Z$

(I used $a , b , \mathmr{and} c$ instead of $x , y , \mathmr{and} z$ when I set up a spreadsheet to do the calculations. Sorry about that).