$$
c^2 = a^2 + b^2 - 2ab \cos(\gamma)
$$
where:
$$
\begin{align*}
c & : \text{third side length} \\
a & : \text{first side length} \\
b & : \text{second side length} \\
\gamma & : \text{angle opposite third side}
\end{align*}
$$
$$
\text{Area}(\triangle) = \frac{1}{2} \cdot a \cdot b \cdot \sin(C)
$$
where:
$$
\begin{align*}
\text{Area}(\triangle) & : \text{Area of the triangle} \\
a & : \text{Length of side } a \\
b & : \text{Length of side } b \\
C & : \text{Angle opposite side } c
\end{align*}
$$
\[
A = \sqrt{s \cdot (s - a) \cdot (s - b) \cdot (s - c)}
\]
where \(s\) is the semi-perimeter, calculated as:
\[
s = \frac{a + b + c}{2}
\]
$$
c = a \cos(B) + b \cos(A)
$$
$$
\begin{align*}
\\
a & : \text{length of side opposite angle } A \\
b & : \text{length of side opposite angle } B \\
c & : \text{length of side opposite angle } C \\
A & : \text{measure of angle opposite side } a \\
B & : \text{measure of angle opposite side } b \\
C & : \text{measure of angle opposite side } c \\
\end{align*}
$$