It sounds like what you really want is the point on the valley floor, not the sloping line, but either way.....
Just create a z aware line with a 3d start point (x,y,z) at the top of you cliff, use some trigonometry to figure out a coordinate that is at 37 degrees well below the surface of the valley floor, and edit the end vertice to be at this coordinate, then either manually record the coordinate where the line intersects the ground surface or use some 3d intersection tool.
If this point will do thats great. I would imagine that you want a line along the valley floor which you could rough out repeating this many times, but you should be able to create a 3D polygon slope that you can intersect with your terrain DEM and come up with a nice line. Make a z-aware line for the crest of the cliff, then copy this line parrallel to itself and modify the z values by a factor that gives the 37 degree slope. Make sure to displace the line horizontally enoungh to ensure the slope will intersect the ground.