Trying to find way to Calculate unsual angle

[Rookio]

Hi Guys,
I'm an architecture student trying to figure out how to calculate the angle at which two pieces of plasterboard need to be mitred in order to achieve a clean cut. This is for accurate presentation in drawing software that gets altered with a few variables. I have attached a picture to try and explain what i'd like to do.

In the picture the 2 red lines are the outside of the plasterboard, one on a raked ceiling, the other on a wall. The two pieces meet at an angle to form a neat mitre.

I know the pitch of the ceiling (20°) , the distance from a known right angle (450mm) and the thickness of the plasterboard sheet (10mm)

I suspect we can acurately calculate the angle of the mitre...but i haven't been able to come up with a solution

Any pointers to get me in the right direction would be a huge help.
Thanks

 

[Rookio]

So my first thoughts are that i will need to determine multiple triangles. and somehow use these to figure out a relationship between thickness of the sheet and the pitch of the roof in order to determine the mitre angle? But after that little tidbit.. i'm a bit lost.

I have added another picture zoomed in to further clarify what i have. Showing the known 10mm and the known 20° pitch. I can draw this up and measure the angles no problem, but that doesn't help me calculate the angle for variouse pitches etc.

Thanks guys

 

[Dr.Peterson]

What you show is correct; you need to bisect the angle between wall and ceiling.

That angle is 20 + 90 = 110; half of that is 55 degrees, and the complement of that is 90 - 55 = 35 degrees.

That's all it takes, unless I'm missing something. The thickness of the sheet is irrelevant, unless the two sheets were different.

 

[Rookio]

That's so typical for me, trying to overcomplicate things.
So simple now that you point it out to me and yes it works perfectly.
Thank you Dr.Peterson