I don't know what method you use, but if you create a tilted plane of 27° that is intermediate to the extrusion that you will then go to make and draw on that plane the profile with the tilted faces laterally of 6° the extrusion you do it without problems. of course the profile must intersect both the cylinder up to its axis and the base that is enough because the extrusion, which you will be intermediate to the plane, intersects completely base and cylinderin the day I will load the file, however the idea of the extrusion of the trapeze for how much I could see is not possible, on a parallel plane to the base plane (circle) of the cylinder because of the inclination of 27 ° extruding on a tilted plane of 27 degrees because the space below the cylinder, at least with my method that is a simple extrusion, would remain empty:
right for the horn: if the tilted part of 27°, in section on a perpendicular plane to the symmetry axis of the inclined wide wall of 27°, must have a rectangular section, to understand us with the edges of the thickness of 10 mm perpendicular to the two broad faces, then the method of callaghan does not work and you have to do the extrusion on the plane as I described. I ask as a rule, in these merging pieces, these profiles are provided in section. rectangles or tilts with dependent corner of the geometry of the piece?I'm closer to the callaghan method.
design the profile of the piece (central view of the attached drawing), then extruded at maximum width and then "excavated" and shape where necessary with extrusions of subtraction.