mitre angles

[joec]

My daughter has asked me to build a wrap around exhaust hood for her new kitchen exhaust fan. From the front it will look square as it goes up to meet the ceiling. From the side it will slope back about 10 degrees from the bottom to the top (the exhaust fan has not been installed yet). Just wondering if the mitre angle for the corners will be at 45 degrees?

 

[Dreuxgrad]

Yes, if you are referring to the angle where the side and front meet; 90 degrees divided by two equals 45,
bevel(top and bottom) cuts will be slope.
I had to learn this as I was trying to picture crown on a portico roof.

 

[joec]

This will be a three sided piece, where the sides butt back into the sheetrock wall. I am referring to the front and sides meet. I was also thinking it has to be 45 degrees.

 

[Gofor]

No. The angle will not be 45 for the miter on the sides with a 10 degree slope on the front. It will be slightly less (on your saw setting) if you consider the blade is at zero when vertical, and the board is horizontal. If you put a try square on a square corner and then rotate it 10 degrees, you will see that the legs of the try square move slightly away from the surface, meaning the angle is more than 90 degrees.. It will only be a degree or two, but enough to make a poor fit.

Time to cut a couple of scrap pieces to dial it in.

 

[Dave Richards]

It might be easier to figure out with a 3D model. As Mark wrote, the angle of the blade will be a little under 45° (the compliment of my ~45.9° angle.

 

[joec]

I knew the smart folks would step up. Thanks.