Planar/disc interaction

[con20or]

Hello all, i wonder if you can help me with a problem I am having.

I have a disc and three planes (representing a road, building and roof). For this problem, the disc can be considered a plane.

http://i3.photobucket.com/albums/y60/con20or/Fig1.png

I know the orientation of each of the planes. The disc is orientated 45horizontal x 45vertical. I can caluate surface normals for each element. With these I can calculate the dihedral angle between the disc and the road, and also the disc and the building, but what I am really looking to find is when looking directly at a vertical surface (middle image) what angle does the plane make on the vertical surface? Its approx 35^ in this case.

This is really bugging me, I'm sure there's an easy way of doing this.

Thanks in advance.

 

[con20or]

i knocked this together in the hope it might illustrate the question a bit better. I am trying to find 'a'.

http://i3.photobucket.com/albums/y60/con20or/image-1.png