I used math today

Building a triangular portico for over the porch on the new house, I knew the width but not the length of the roof pieces.


C(2) = A(2) + B(2), so I just took a square root. Everything seems to line up. Can't recall using geometry since high school.

I guess the need you have for various mathematics depends on your job to a great extent. I have used geometry in various house repairs and modifications (and for such things as calculating compression ratios on racing engines). That's probably very common. But in my work, I have used geometry as well as algebra, trigonometry, logarithms, and even calculus. I think most people use algebra from time to time without realizing it.

Carpenters, especially framers, are always using 3-4-5 triangles to square up large assembled pieces.  One time we had an oddly shaped construction and the 3-4-5 was awkward to lay out.  I suggested using a 5-12-13 — oh no, that's ridiculous, every knows it's 3-4-5.  I even proved it with the Pythagorean formula and they still wouldn't buy it.  Another time a foreman wouldn't accept that 6-8-10 was acceptable.  Good times.

The portico I'm building will tie into the existing roof. The 45° roof over the porch will be attached to the standard 4/12 roof pitch on the house.

I can't even CONCEIVE of the angles that will involve. I plan to eyeball it on-site

You can lay out every cut with just a framing square — it's an amazing analog calculator. But builders with that sort of knowledge anymore are rare. Lots of guys use computer programs to arrive at the dimension of framing parts. But for your project eyeballing will probably be sufficient. One thing that might help is having a full sheet of smooth plywood which you can use to draw scaled-down representations of the angles. You can also cut some boards into scaled-down pieces of lumber and do your cutting and fitting on a 3D model and transfer the bevels to the lumber when you're satisfied with the fit.