What's my sine?

[boco]

This is embarrassing, but I need someone to check my math. I will be cutting a bevel for the first time at anything other than 45 degrees. I am planning a pedestal that is essentially a sawed-off pyramid. The base and top are squares (11” and 5.5” on a side, respectively). The four side panels are trapezoids tilted on an angle toward the center. The question is, what is that angle? I’m sure that when I was in high school I could have solved this in 60 seconds, but that was longer ago than I care to remember and the synapses just don’t fire the way they used to.

Here is a side view in two dimensions (not exactly to scale).

Pedestal angles.jpg (24.63 KiB) Viewed 6658 times

Angle C is a right angle. I calculated the value of Angle A by dividing the length of the side opposite that angle by the length of the hypotenuse, then used a calculator to get the inverse sine of that number. I came up with 62.72 degrees, which I think is the angle at which I need to miter the sides and bevel the top and bottom of the panels (plus a 45 degree bevel on the sides of the panels) to get it to fit together. I’m going to cut some test boards, but before I do, can anybody confirm that’s the right answer or tell me where I went astray? Thanks!

[S Brian]

Angle B = Side adjacent/Side opposite = Sine B

Angle B = 2.75/6 = Sine 0.458333

Sine 0.458333 = 27°17'

Angle A = 62°43'

The angle is actually a few seconds under 27°17' and a few seconds more than 62°43', but I think this is good enough for woodworking.

[algale]

Boco: I think your math is correct for a two dimensional shape as shown on the diagram but this is essentially a tapered, splayed shape you are building and you need to make compound miter cuts. Go here for a table. http://woodgears.ca/miter/index.html

S Brian: Sine is opposite/hypotenuse NOT adjacent/opposite. SohCahToa http://www.mathwords.com/s/sohcahtoa.htm

[JPG]

Beware! If you bevel the edges, you create a compound angle. 45 degress only works with a right angle.

I defer to those who have delved into compound tables before.

[rjent]

Is there going to be a test on this ......

[boco]

Thanks for the link to the table, algale. Clearly this is more complicated than I thought (and I thought it was pretty complicated....)

Is there going to be a test on this ......

Only for me! I'll let you know how it turns out.

[masonsailor2]

It' won't be that bad. You now have the angle of the bevel. Create a sled ( or modify one you already have ) to securely hold the piece at the compound angle. The Shopsmith actual is a great tool for this function. The fun part is clamping it while the glue dries !
Paul