Q:

How do you calculate the voltage between two phases? 

If I have two hot wires at given voltages and phases (for example 120v 0deg and 120v 120deg), how do I calculate the voltage between the two wires? 

A:

You really have to think about this as vectors...

With a little trigonometry you can calculate the length of the hypotenuse as.. 
\$=\sqrt{(Sin(\Theta).V)^2 + (V(1-Cos(\Theta)))^2}\$

