Stupid math question

If I have a 45° angle piece, and it travels downward perpinducular to level, and the length of the piece needs to go 31"… how long of a piece would I need?

Wait I should just draw this out. It’s for my pond and the PVC contraption I need to do. I need to figure out what both green line values need to be.

If you ignore the length of the 45 angle segments and couplings (and I assume a 90 degree angle at the top of the right blue), then the top green is 31" * sqrt(2)

edit: oh, left green is almost nothing, like 2"? (~ 43 - 31 - 10.5)

I get 43.8" for the diagonal line, and 1.5" for the short straight line, ignoring the lengths of the angle couplings.

Method: If you draw a line from the left 45 degree angle horizontally, you create a 45-45-90 triangle, with each of the short sides being 31" and the long side being ???. Using the pythagorean theorem, you get sqrt(961 + 961), which is 43.8. Then, once you know that the other side has to be 31", you can see that the horizontal line has to be only 12" from the bottom of the diagram, so you just need to add 1.5" to the existing side.

The top of the right blue (the red) is a 45­­° than goes along the green to the other red 45° angle that then leads down to the blue 10.5" piece. The bottom two blue corners are 90° angles.


43.83" (or 43 & 10/12") and 1 1/2" like Thraeg.

Sure, but the top right red-“45” meets the blue at a 90 degree so there should be another 90 degree coupling there.

Oh I’m sorry, the 43" height is just the height/side of the pond. The pipe actually goes straight out from the 45° coupling piece.

Ok, that’s clear now. Numbers above work out. You should have probably added some frops for a sense of scale ;)

Equilateral triangles have all three sides the same and all angles 60 degrees.

Oops you’re right. I meant Isosceles. Pardon the brain fart.

My approach would be “PVC pipe is pretty cheap I’ll just cut it a little longer than what I think is right and if it’s too long I’ll just cut a little more off!”

I would normally do that except it’s all underwater, and I can’t see more than 2" down right now. I have a crate with netting that has to rest in the deepest part of my pond to try and keep my fish from getting sucked into the PVC tubing.

Oh yeah, being underwater does complicate things. But you could always assemble it in your yard and then glue it and stick it underwater at the end. But you should obviously do it however you want. I give you my permission!

lololol :)

I recommend this program if a similar problem arises in the future:

Thanks, that’s probably better than the one I was going to use:


Oops, I meant this one specifically:

90% of it is point-and-click using the mouse. I’ve been using this or similar software since the late 1990s to create art or sketch out and model problems in 3D scenes.

I too have a dumb math question, except it’s about terminology:

Is there a term (similar to the numerator/denominator distinction for fractions) for everything to the left/right of a minus sign? ie how do I describe all the things that are (in this case) aggregated, before a bunch of stuff is subtracted from it.?