Help with miter angles

[Jared Cuneo]

I have a commission for a small coffin shaped box and came across this image, but the miter angles don't add up.

I've made a plan in sketchup which I can use with some trial and error, but I was wondering if anyone knew what was going on here....

Thanks!

JC

[Bob Vallaster]

...get them angles?
You're working with a hexagon. The included angle at each corner on a hex with equal sides would be 120*. Yours has sides of various length, but the sum of the angles will still be 6x120*=720*. That's as far as I'll go on doing math in public.
I suggest you do some modeling. Use a few yardsticks, some long/skinny scrap or cut strips of cardboard to outline what looks right in shape and proportion. Tape/pin it to the table when you have what you want. Use a protracter to measure your angles. Make notes and check the sum (=720*?). Bevel at each respective corner should be half the included angle.

Bob V.

[Chris Bruno]

I have a commission for a small coffin shaped box and came across this image, but the miter angles don't add up.

I've made a plan in sketchup which I can use with some trial and error, but I was wondering if anyone knew what was going on here....

Thanks!

JC


Hi Jared,

Their angles are definitely incorrect (and maybe even some of the lengths), but its pretty easy to calculate the correct angles with a little trigonometry.

I hope this doesn't come across as 'talking down', but I figure may be some people would be happy with a little trig refresher:

Take a look at the top portion first. 17" wide at the top,
28" wide at the bottom and 21" tall. Draw two vertical lines down from the edges of your top line to the line that would cross the horizontal. This will leave you with a right triangle that is 21" tall, and has a 5.5" wide base. (28-17)/2= 5.5

[See pic 1]

Now some easy math. The hypotenuse of that triangle is the square root of the sum of the squared sides. That is sqrt (5.5^2 + 21^2). I get a length of 21.7".

[see pic 2]

You can also calculate the angles easily. Remember that old pnemonic (sp?) SOHCAHTOA? Sine=Opposite/Hypotenuse..etc. so the calculation of angle 'a' would be:

tan (a) = 21/5.5
a = Atan (21/5.5)
a = 75 degrees

Since all the angles of a right triangle add up to 180, then the angle at the top would be:

b = 180-90-75
b = 15 degrees

Figuring out the angles for the rest of the coffin should be pretty straight forward.

Now, as is the case with all 'online-math', I hope I didn't screw it up! ;)

Hope this helps,
-Chris

[Doug Shepard]

Is it possible that image you have is for something with sloped sides so that there's some wierd compound angle stuff going on but you're only seeing the angles with respect to one plane?

[Jared Cuneo]

Well, after some calculating, I've determined that if you use 75 degree miters in the middle, that the ends will always work out to 52.5 degrees, no matter what the length....

JC

[Will Blick]

Although I have had my fair share of math in my day, bottom line is, you forget, you make mistakes, you're tired, etc.

I downloaded a program called Microsoft Math, has a simple Triangle solver sub program.... its so easy, no more thinkin...

IIRC, I think it was $20.... well worth it, as it also has an equation solver, which I use all the time, very easy and intuitive.