What is the distance from the origin to a right angled regular hyperbolic octagon? Given a right angled regular hyperbolic octagon centered at origin, what is the distance from the origin to any vertex?
I know that the distance between the origin and the point $p=(a,0)$, $a>0$, can be solved using the metric $g = \frac{4}{(1-x^2-y^2)^2}(dx^2+dy^2)$. But how will I figure out where $g$ is?

"The Geometry and Spectra of Compact Riemann Surfaces" by Peter Buser has a great section on Hyperbolic trigonometry. Chapter Two  has the relevant material, although the whole book is great. 
