I have a graphics problem that reduces to this:
(Computer equation)
alpha = arctan(X / ((Y / (Z * cos(alpha) - k)) * Z * cos(alpha)))
(LaTeX)
$\alpha = \arctan \left( \displaystyle \frac{x}{\displaystyle \left( \frac{yz\cos(\alpha)}{z\cos(\alpha)-k} \right)} \right)$
I need to solve for $\alpha$. Obviously, there's no closed form. I know $\alpha$ is around $13.5^{\circ}$. Is it "wimpy" of me just to use $13.5$ on the right hand side to get an approximation? Or would "a real man" use Newton-Raphson, or bisection, or something?