Remember that vectors can always be moved around. What you need to do is to, say, start with the T at an angle, add (vectorally) that to the T that is vertical, and that will determine the resultant (your green R.) That will give you the triangle you are interested in. The problem with this approach (and any other approach) is that we have no angles to put into the formulas. All we have is a value for T, but we can't resolve the T's into components without an angle.

Resolving forces is breaking them down into vector components. Equilibrium problems are set up by noting there is no net force in the problem, meaning that all the forces add up to be 0. In your case we have (This means that the direction of the green R is incorrect. It should be pointing "up" and to the right.)

-Dan