# Calculating Angles during Design



## woodsdog (Dec 8, 2012)

I am trying to recreate an arcade control panel. In doing so I am using Google Sketchup. I have gotten to a point where I need some help in calculating angles.

I am trying to create a base using 3/4" by 5" high wood. The base isn't a standard shape, and I need to mitre the edges together. I am having a really hard time figuring out how to calculate the angles I would need to cut.

I have a picture, it will help show what I am trying to explain. I need to connect the piece labeled angle A to Angle B (obviously on both sides). The measurements from the midpoint of the 3/4" boards to the midpoint of the 3/4" bottom board is 9.5". The angle of the line that connects the midpoints is 41.7 degrees.

Can someone help me understand how to figure out the angles or implement them?


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## cabinetman (Jul 5, 2007)

I don't do Sketchup, but I can tell you how I find angles like that. You can connect A to B, and use a protractor on the obtuse angle, and divide by 2 for the angles of each leg.

Or, for the thickness of the walls of the legs, continue the outside lines for each leg of the angle until they cross each other. Bisect the angles where they do that. You will have the angle for each leg. A protractor will give you the degrees.













 







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## mdntrdr (Dec 22, 2009)

SketchUp has a protractor tool that will read/set any angle you like.:smile:


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## subdajj (Mar 9, 2013)

mdntrdr said:


> SketchUp has a protractor tool that will read/set any angle you like.:smile:


"x2"


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## woodsdog (Dec 8, 2012)

Just wanted to say thanks to cabinentman, your advice helped.

I am/was aware of the protractor tool in Sketchup, but I needed help with it. 


For the curious, he's the angles put into place:


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## cabinetman (Jul 5, 2007)

woodsdog said:


> Just wanted to say thanks to cabinentman, your advice helped.
> 
> I am/was aware of the protractor tool in Sketchup, but I needed help with it.
> 
> ...


What did they work out to?









 







.


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## woodsdog (Dec 8, 2012)

Angle A was 66 degrees. Angle B was 64 degrees. Of course, the angle depends on how you position it..

I thought they would both be the same, but I think compensating on one side a little offset the other just a bit. 

I think once I get it out there and cut a degree or two won't matter.

Thanks again.

EDIT: After writing that, I don't know why i didn't try 65 degrees on both sides. maybe i will go back and mess with it.


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## nostrildamus (Feb 24, 2009)

For future reference:
If you have a right triangle, and you're looking for the angle, call it X, the tangent of X is the opposite side over the adjacent side. So, in your project, lets say the vertical portion from "Angle A" to "Angle B" is 3 inches, and the horizontal portion is 4 inches. Tan (B) is 3/4. If you have a calculator with an inverse tangent function (Tan-1) it will give you the answer (36.8 degrees in this example). If your calculator has only a regular tangent function (the iPhone has this) you can get the answer by successive approximation. Split the angle in half to make miters.


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## rmack (Apr 25, 2013)

Off the cuff, I believe each of those angles are 22.5 degrees.


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## msbeal (Oct 3, 2010)

*Did you solve your problem?*

The problem is similar to installing baseboards around angled walls. There is a book I use called Crown Molding and Trim by Wayne Drake. 

Wayne is a retired engineer who took a real shine to this very problem working both with baseboards and crown molding. His book comes with charts to look up the exact miter angle you use on your saw for any turn (horizontal like yours or vertical turns). 

If I weren't knee deep in my own projects right now I'd offer to reacquaint myself with the problem for you. 

Anyway, anyone who runs up against these issues often should look into the book. www.compoundmiter.com

One time I was up against an issue and emailed Wayne. The gentlemen had no problem helping me out. Sweet.


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## msbeal (Oct 3, 2010)

*To rmack*

I just did a quick look up in that book I mentioned and according to my reading the miter angle you set on your saw is 20.5 degrees. 

So your eye is very, very close (or maybe even right for all I know). I wish I had the time to reread the first two chapters to do this guy's problem justice but I'm on the run right now. 

To find the length you'd need just measure from outside tip to outside tip and lay out the length you need on your board after marking the angles.


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## woodsdog (Dec 8, 2012)

Just a follow-up, if anyone is curious. I doubt they are, but I thought it'd be cool to do an update.

So the picture and design in the original picture needed to be updated, it wasn't quite right. The original angle on that one was said to be 26 or so. After I redid it a little (wrong sizes, wasn't quite what I wanted), I redid the math, and it actually turned out to be 22.5 degree angles. So rmack was right on what I actually did. That amazes me.

I ended up using some deck hardware that was at a 22.5 degree angle to help stabilize it. It worked great.

Anyways, here is a picture of it actually built. It's not as square as I would like, but it works just great. 

I really appreciated the help offered here. The math I used from here was right one. Thanks again.


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