Determining intersection between eaves and sun path vector

Hi everyone, I am very new to grasshopper so I hope this question is not too foolish, or strangely constructed. 

Basically as the picture indicates I have a simple form with an extending roof and a vector indicating sunpath to the bottom of where the window will be. What I am trying to achieve is to get the eaves of the roof to automatically extend the required distance to prevent direct sunlight from touching the bottom of the window.

As you can see in the second image I initially tried to do this by defining a triangle between the bottom of the window, the corner of the eaves and wall, and the line between the end of the eaves and the base of the window then using sine rule to determine what the length of the eave should be.

It doesn't seem to work, no combination or manipulation of the value for the angles seems to create an eave length that matches the distance to the vector, furthermore if I change the value of the roof angle the length of the eave changes erratically. 

Unfortunately I do not have the background in maths to solve this problem elegantly, I am limited to using conceptually simple but mechanically clunky methods. Thanks in advance for any help.