Planar/disc interaction

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Hello all, i wonder if you can help me with a problem im 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 im 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 theres an easy way of doing this.

Thanks in advance.
 

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