A layout calculation question

[jpdv]

Folks,

I am adding a room in the new house. All gone well, down to trim and coving. To be in keeping with some of the other rooms, the door is tight against a wall. The final trim that will go around it will be 'standard size' on the other (non-wall) side and the top, so these 2 will meet with a normal 45 degree mitre. The trim on the wall side is wider, so as to go right flush to the wall. It's been 'a few' years since my school trigonometry - other than trial and error, what is the formula to work out the mating angles for a mitre with 2 pieces of unequal width? I'm sure there's a sine or a tangent in there somewhere - help me, brains trust!

[Skew ChiDAMN!!]

SOH CAH TOA ring a bell?

SinX = Opposite/Hypotenuse
CosX = Adjacent/Hypotenuse
TanX = Opposite/Adjacent

But why go that way? If the trim for both widths have the same profile (eg. bullnosed) just different widths, then the profile won't necessarily match. Marking where the skinnier trim intersects the side of the wider trim and then cutting 45° keeps it simple AND the profile should match.

[jpdv]

Happy with the base maths mate - 'See old Harry Catch a Herring, Trawling off America' was my learning... But nope, it's completely flat 'molding', so the only issue is avoiding a spur sticking out to one side (which occurs if I make the mitre at 45 degrees...). I will probably just eyeball and adjust - but I bet there's a layout calc somewhere in one of those carpenters' pocketbooks...
If, for example, one piece were twice as wide as the other, would I make the cut at an angle half way between 45 and 90 degrees? I don't know off the top of my head... (obviously, mating cuts, so one larger by half, one smaller...) Also obviously, I know the width of both pieces. It's a bit like crown moulding on non-square corners, I suspect.

[ErrolFlynn]

Chances are if you were able to calculate angles and line lengths, and got them perfect, by the time you transfer those calculations to your mitre saw, you’d never get the angle right and it would still look wrong. Anyway, chances are the angle would be something you’d never be able to setup (eg. 21.12 degrees or something equally unobtainable).

If I were doing this I might get myself a couple of bits of paper cut or folded to the same dimensions then lay one over the other to highlight the correct angle. Then I’d use that as a starting point for the trial and error notion with some scrap materials.

[Beardy]

Rather than calculate it out just grab your two different widths and mark it out on a piece full size if board or paper and replcate the angle to use on your saw
Depending on the width you often still stick with 45 degrees and plumb cut the excess to the wall face

[jpdv]

I like that Beardy - I reckon I'll go with the plumb cut option. Thanks.

[Chief Tiff]

TOA;

Where Opposite is the width of the narrow piece and Adjacent is the width of the thicker piece.

I always have a scientific calculator on the bench so that would be my first choice; otherwise as Beardy says just draw it out and transfer the angle to the mitre saw using a bevel gauge.

[clear out]

If you have a couple of short offcuts use them to dummy it up.
H.

[Fuzzie]

I've had a couple of homes where this has been done the way Skew described with the cuts at 45°. It seemed the common carpentry practice as far as I know.

You could also adapt the method shown for fixing other out of square problems as shown it this video:

https://www.youtube.com/watch?v=Y8rtYbKoook

[rustynail]

As the side adjacent to the wall will carry the wider architrave this will be the longer when cut at 45*. Therefore it will be a level cut to remove the horn sticking beyond the 45* cut on the standard top architrave. Nothing looks worse than odd angles on door architraves. It makes them all look wrong and they are wrong if there is grain figure or moulding detail to be considered.

[jpdv]

For anyone facing the same issue in the future, Rusty and Beardy were spot on. I went with 45 degrees and trimmed the 'horn' on the wider piece flush. Looks very tidy. 'Keep it simple stupid' wins the day...