Calculate angles on slanted wall under slanted ceiling

[Kristofferm]

This is something for the math geniuses on the forum to figure out.

I'm working on framing a wall that is at a 45-degree angle against a roof that is 41.5(?) degrees. I was hoping to use some math to figure out the angles at which to cut the posts, but it wasn't entirely straightforward.

Another complication for me is that the adjoining walls are right-angled (I'm building a rectangular room where one corner is cut off at 45 degrees) and the angle of the top plate differs from each other at the two meetings with the adjoining walls.
In connection with the wall running parallel to the outer wall and ridge, it's 41.5 degrees, whereas at the meeting with the wall running between the ridge and outer wall it's perhaps around 30 degrees.

So, according to my understanding, this means that the angles at which the vertical studs on the 45-degree wall should be cut will vary depending on where on the wall they are?

 

[Pumabjörnen]

This is something for the forum's math geniuses to puzzle over.

I'm in the process of framing a wall that is at a 45-degree angle to a ceiling that is 41.5(?) degrees. I had hoped to use a bit of math to figure out the angles to cut the studs at, but it wasn't entirely easy.

Something that's complicating things for me is also that the adjoining walls are right-angled (I'm building a rectangular room where one corner is cut at 45 degrees) and that the angle of the top plate differs at the two junctions with the adjoining walls.
In conjunction with the wall that runs parallel to the outer wall and ridge, it is 41.5 degrees, whereas at the junction with the wall that runs between the ridge and the outer wall, it may be around 30 degrees.

According to my head, this should mean that the angles at which the standing studs on the 45-degree wall should be cut will vary depending on where on the wall they are to be placed?

Will the wall you're building somehow offload any other wall/ceiling?

 

[Kristofferm]

Should the wall you are building in any way support another wall/ceiling?

No, but it will be tiled, so it needs to be stable.

 

[Pumabjörnen]

No, but it needs to be tiled, so it needs to be stable.

Have you already bought the studs for the wall?
If not, I advise you to use metal studs and tracks, much easier to work with when it comes to angles imo, especially if the wall is not load-bearing in any way.

The type of stability you seek for the tiles is not achieved by whether the stud in the wall is under "tension" but through the correct stud spacing and proper backing material.

 

[Kane]

You have a miter saw, right? Take a piece of scrap lumber and set the known angles (45 and 41.5?) on it and test.

 

[Kristofferm]

You have a mitre saw, right? Take a scrap piece of wood and set the angles that are known (45 and 41.5?) on it and test.

Yes, that's exactly what I wanted to avoid.

Since it's 45 degrees diagonally over another angled surface, the known angles don't help. I end up somewhere near 30/30 degrees on the first piece.

 

[Kane]

Yes, that is exactly what I would have liked to avoid.

Since it's 45 degrees diagonally over another angled surface, the known angles don't help. I end up somewhere near 30/30 degrees on the first rule.

Now I drew it up in 3D, and it should be 32/32 with a 41.5-degree roof pitch and 45-degree wall angle. Have you figured it out yourself now with a bit of testing?

 

[Kristofferm]

Now I drew it up in 3D and it should be 32/32 with a 41.5 degree roof pitch and 45 degree wall angle. Have you figured it out yourself now with some testing?

I ended up at 29/31 degrees with about half a degree plus/minus in difference. There are no exact angles in a house from 1951.

The angles were also the same all the way through, it was an optical illusion that it would be something else. It took a bit of swearing and a couple of miscuts before I got everything to fit.

Using metal overhang, as Pumabjörnen recommended, would probably have been convenient.