$$ \newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\dx}{\text{ dx}}
\newcommand{\rang}{\text{rang}}
\newcommand{\s}{\ \ \ \ \ \ }
\newcommand{\arrows}{\s \Leftrightarrow \s}
\newcommand{\Arrows}{\s \Longleftrightarrow \s}
\newcommand{\arrow}{\s \Rightarrow \s}
\newcommand{\c}{\bcancel}
\newcommand{\v}[2]{
\begin{pmatrix}
#1 \\
#2 \\
\end{pmatrix}
}
\newcommand{\vt}[3]{
\begin{pmatrix}
#1 \\
#2 \\
#3 \\
\end{pmatrix}
}
\newcommand{\stack}[2]{
\substack{
#1 \\
#2
}
}
\newcommand{\atom}[3]{
\substack{
#1 \\
#2
}
\ce{#3}
}
$$
Law of Cosines
![300](../../images/pasted-image-20230621111948.png)
$$a^{2} = b^{2} + c^{2} - 2bc \cos(A)$$
$$b^{2} = a^{2} + c^{2} - 2ac \cos(B)$$
$$c^{2} = a^{2} + b^{2} - 2ab \cos(C)$$
also
$$\frac{a}{\sin A} = \frac{b}{\sin{B}} = \frac{c}{\sin C}$$
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