Given three vectors: $|\vec A| = 2850$ and forms a $150^\circ$ angle with the positive $x$-axis, $|\vec B| = 650$ and forms a $60^\circ$ angle with the positive $x$-axis, $\vec C$ which has a positive $x$-component and zero $y$-component. I need to find the minimum and maximum values of $|\vec C|$ such that $|\vec A + \vec B + \vec C| \le 2400$.

I initially thought about using law of cosines,

\begin{align\*} 
|\vec A + \vec B|^2 &= |\vec A|^2 + |\vec B|^2 - 2|\vec A||\vec B|\cos 90^\circ \\
|\vec A + \vec B|^2 &= 2850^2 + 650^2 - 0 \\
|\vec A + \vec B| &\approx 2923.183 \\
\end{align\*}

And I could repeat this using $|\vec A + \vec B|$ and $|\vec C|$, to see what value of $|\vec C|$ gives me $2400$, but I don't see how this gives me the minimum and maximum possible values.

What approach should I be taking to find the min and max values?