Math question for collar beam angle?

[Lennyzx11]

What’s a math or framing/speed square way to solve for the
Collar beam to principal rafter angle in order for it to end up level?
I’d like to cut the 1” housing appropriately also.
Do I cut the mortise square to the rafter or also angled? 
With 45° degrees such as braces it works itself out but I’m having trouble converting to the 9:12 pitch I’m using.

This coincides with making the post to rafter connection plumb but I think that just means cutting the top of the post at the 9:12 slope/pitch.



 

Thank you,
Lenny

[GRadice]

If I understand your question correctly, the angle at the end of the collar tie is also 9/12, the same as the roof pitch and the same as the angle on the top of the vertical post.

I can't answer your question about the mortise and tenon since I have no experience with something like that.

[Don P]

There's several ways.

Math;
Pitch angle= atan(rise/run)=36.86°
Deduct that from 90° to get the complimentary angle=53.14
Remember the sides of a triangle add up to 180°

Framing square, this is the real way in the field. 12" on the blade, 9 on the tongue. The tongue is the plumb cut, the blade is the level, seat cut.


 

With a speed square you can pull angles from the framing square layouts and read degrees;


 

 


Draw it to scale and use a protractor, or in software a protractor function;


 

I'm sure there are more.

[Lennyzx11]

Thanks DonP. 
That’s what I was looking for.
That way(s) seems much more efficient than cutting the d*** thing three times wrong.

[Prizl tha Chizl]

Don’t worry, we’ve all been there. (At least I have-more than once, usually on those valley  rafters.)

My uncle’s adage
“I cut it three times-and it’s still too short!”