# Angle formula for fitting X-frame



## RichO (Apr 29, 2009)

Hey guys,

I am making an X-frame for a wine rack similar to this drawing?










For instance, if this opening is 12 wide and 16 high, is there an easy way to come up with the angles for the blade tilt when cutting the corners of the X, for whatever the dimensions of the rectangle are? Seems kind of tricky but maybe someone has a shortcut.

Thanks


----------



## Steve Neul (Sep 2, 2011)

Draw it out full scale put a protractor on it. Drawing it not only will give you the angle but the size of the parts.


----------



## woodnthings (Jan 24, 2009)

*a mathematical approach*

If you know the length of two sides or a right triangle, you can determine the angle:
http://www.mathsisfun.com/algebra/trig-finding-angle-right-triangle.html

Two parallel lines transversed by a diagonal line, the opposite angles are equal:
http://www.mathwarehouse.com/geometry/angle/parallel-lines-cut-transversal.php


----------



## m.n.j.chell (May 12, 2016)

Make it easy, and easily repeatable, on yourself. Just make square boxes and go with 90 and 45 degree angles.


----------



## RichO (Apr 29, 2009)

Thanks for the replies. I was able to get this one to turn out nearly square so it worked out but if I have to do another one that fits in a rectangle space I will have to do a lot more thinking on it.


----------



## FrankC (Aug 24, 2012)

Not really a lot of thinking, just draw your rectangle on one edge of a sheet of plywood, add the diagonal lines and you have the two angles you need for the cuts. You can transfer them to your saw using a sliding bevel tool.


----------



## ronbergley (May 19, 2014)

cosine of the angle is equal to the adjacent side divided by the hypotenuse when working with a right triangle. You can the arcosine to get the angle. Just use a scientific calculator.

Ron
Quality Custom Interiors


----------



## FrankC (Aug 24, 2012)

In most cases it is not the numbers that matter but the fit, and all too often it is the numbers that lead us astray.


----------



## GeorgeC (Jul 30, 2008)

There is no equation that does what you want. Each time you build this to new dimensions it will be different.

Your simplest solution (and very easy as well) is measure the angles each time you build. This was you cannot go wrong.

Or just make each leg one inch too long. Lay the "X" across the box you want to fit it into. Take pencil and mark angle on legs. Cut.

George


----------



## TomCT2 (May 16, 2014)

RichO said:


> Thanks for the replies. I was able to get this one to turn out nearly square so it worked out but if I have to do another one that fits in a rectangle space I will have to do a lot more thinking on it.


it is simple geometry. the only glitch is you need to be able to find the angle from the tangent value computed.

for example, the lower left bottom corner... the angle of the line to the upper right top corner....
tangent of angle = length of opposite side divided by length of adjacent side
i.e. tangent = 16/12 = 1.33333. there are a few billions internet sites that will tell you that the arctangent (aka tan-1) of 1.333 is 53.13010235 degrees. 

plug "tan-1(1.3333) in degrees" into Bing, for example. you will find difference at 3-4-5th decimal place depending on how the rounding is done.

you can calculate the angle of the top in a similar fashion, 
or - 
knowing that the three angles inside a triangle always add up to 180 degrees, , , , 
180 minus 53.13 minus 90 (the bottom right...) = 36.86989765 etc etc. 
which is not approximate, or sort of, or close to .... that is exact.

the Greeks knew how to do this stuff. they refined geometry theories that go back some to 3000 yrs BC.
it's not fusion rocket propulsion as some would have you believe. the "equations" exists are are quite well known to people who are not blowhard idiots. the equations do not change every time somebody builds something.

if you have a digital protractor you can get the saw set real cotton picking close - but I'd advise cutting some scrap ends to be sure the tilt is mechanically set "right on"

the geometry and the math is really the easy part. if you have only one table saw, you can cut the length needed (ye' olde a^2+b^2=c^2 thing) - but repeating the angle cuts to "exactly the center line" is the real problem.


----------



## Brian(J) (Feb 22, 2016)

I have tried to make the math work a few times but in practice it hasn't worked out as well as drawing it full size and scribing it.
Most designers will draw it in a CAD program of some kind and then just use the angle indicator tool to instantly calculate the angle. That's what I do now, and it takes less than a minute.


----------



## TomCT2 (May 16, 2014)

yup. that's how the Egyptians built the pyramids - they first drew out the design full size on papyrus and transferred the angles to the stone quarry. giggle.

wonder how the CAD programs come up with the angle? wait! I know!!! geometry!


----------



## m.n.j.chell (May 12, 2016)

"fusion rocket propulsion" ???

Did someone develop an atomic rocket engine and not tell the world?


----------

