[Abekkus]

....There's no trigonometry in common roof-slope-area calculations and designations, only pythagoreans. Rise over run, 6ft for every 12ft, etc.

I do feel your pain about vetting "professionals", especially living in a place that tries to prevent me from making my own improvements.

[alt227]

Arent sloped roofs just rectangles?

[ncallaway]

The intersections of the joists/beams and the rafters require you to cut angled cuts on the rafters to sit appropriately on the joists/beams.

See: https://www.structuralbasics.com/rafter-roof-design/ and imagine how you would get a rectangular piece of wood for the rafter to sit flush against the rectangular joists/beams.

[SoftTalker]

OK there might be some confusion here on what's meant by "roofer." Roofers as I have always seen the term used means the crew that puts the shingles on.

The roof structure is built by carpenters or framers. Or more likely just delivered as pre-built trusses which are placed on top of the walls.

For a roof built on-site, a speed-square or framing square will include markings for common roofing cuts, hip/valley cuts, etc. You have to know how to use them but you don't really need to understand the underlying trigonometry.