I'm trying to replace the cove molding around the hearth. As u can see from the pic, there should be a vertical molding running up the wall, a short horizontal piece running across the brick, and a longer piece running along the vaulted ceiling. I already got the angles for the vertical and short horizontal piece. But I'm having trouble making the correct angle for the short piece to vaulted ceiling corner.

I found the formulas below on Rake Crown Moulding Miter Angles . The spring angle of the cove molding is 45°. I calculated the roof pitch angle as such:

Height of south wall is 94”. Height of south side of hearth is 108.5”. Distance between them is 115”. So it’s 108.5-94=14.5”. Tangent is defined as opposite divided by adjacent, so that’s tan X = 14.5/115, and X = 7.18°

Trigonometric Crown Angle Formulas for Vertical Plane Crown Molding Angles (cathedral/vaulted ceilings/rake gables)

Crown Miter Angle = arctan (cos( Spring Angle) ÷ tan((180° - (Roof Pitch Angle * 2)) ÷ 2 ))

And, just like math class, here is where I show my work:

Crown Miter Angle = arctan (cos( Spring Angle) ÷ tan((180° - (Roof Pitch Angle * 2)) ÷ 2 ))

Miter angle = arctan (cos 45°) ÷ tan((180°-(7.2° * 2)) ÷ 2))

Miter angle = arctan (0.70710678118654752440084436210485) ÷ tan((165.6) ÷ 2))

Miter angle = arctan (0.70710678118654752440084436210485) ÷ tan(82.8)

Miter angle = arctan (0.70710678118654752440084436210485) ÷ 7.9158150883058268442674417219033

Miter angle = 35.264389682754654315377000330019 ÷ 7.9158150883058268442674417219033

Miter angle = 4.45°

Crown Bevel Angle = arcsin (sin( Spring Angle ) * cos((180° - (Roof Pitch Angle * 2)) ÷ 2))

Bevel Angle = arcsin (sin( 45°) * cos((180° - (7.2° * 2)) ÷ 2))

Bevel Angle = arcsin (0.70710678118654752440084436210485) * cos((165.6)) ÷ 2))

Bevel Angle = arcsin (0.70710678118654752440084436210485) * cos(82.8))

Bevel Angle = arcsin (0.70710678118654752440084436210485 * 0.12533323356430424537311875981651)

Bevel Angle = 5.08°

A couple things I thought of:

1) Am I following the correct order of the parentheses? I went thru it several times and I think I am.

2) Do these formulas assume that the molding is laying flat or pushed up against the fence of the miter saw? Other formulas on the same page assume the molding is laying flat. I also tried pushing it against the fence, but that didn't work either.

3)The angle from the wall to the vaulted ceiling is technically 97.2°. So I tried that rather than 7.2°, but that didn't work either.

By experimenting, it looks to me like a miter angle of 25° and a bevel of 30° is pretty close. And that is nowhere near the numbers I've got from any of the things I've tried w/ the formulas.