How to make an angle?

[Lynden]

Buy an adjustable triangle. You'll find lots of uses for it.

https://www.amazon.com/Alvin-110C-10-Adj...B000HEOHBC

http://www.rockler.com/woodworkers-adjustable-triangle

[Paul-in-Plymouth]

You already have a lot of good practical advice from Rob Young and others.  Your question suggests that you might find this useful to think about in addition.

Angular relationships are commonly expressed a couple different ways:  as the angle itself or as the tangent of the angle (or its equivalent: pitch, rise-over-run, slope, etc.).  These specify the same thing, but it’s not necessarily easy to go from one representation to the other without a calculator or trig table or a protractor.

Values of angles are easy to talk about in designing something, but for the angle to be useful in making something, say for setting a sliding bevel, you need its tangent.  So, Chris can tell us 10º, and we’re stuck without something else to translate for us, be it protractor or trig table or calculator.   As you discovered.

However, for small angles, say less than about 15º, there is a very simple way to do the translation:  the angle itself is a good approximation of its own tangent, if the angle is expressed in radians and not in degrees.  It’s so simple that it often becomes a head calculation.  

A radian is 180º/pi or 57.295....º.  Immediately, that’s complicated.  But if I start with the Biblical approximation for pi, namely 3, it becomes arithmetic even I can do in my head:  60º.  And I just have to remember that because I’ve lopped about 5% off the value of pi, the estimated size of my radian at 60º is about 5% too large, and the tangent I estimate with it will be 5% too small.  If need be, I can fix that later.

So, tan 10º ≈ 10º/57.3º ≈ 10º/60º = 0.16667 or an integer ratio of exactly 1:6.

I can look up the precise angle corresponding to  a tangent of 0.16667 and find it’s 9.46º.  Not bad, but if I  correct the tangent up by 5% for the error introduced by truncating pi to 3, then I get  the tangent estimated to be 0.175, corresponding to 9.93º, pretty close to 10º for an approximation calculated in my head.  Versus 0.176 for the tabulated tangent of precisely 10º.  

Maybe Chris actually wanted a precise 10º splay.  But maybe instead, Chris thought a splay of about 1:6 for these legs would represent a good compromise of everything in this design - strength, stability, not inadvertently sawing the legs off, etc. -  and that’s almost 10º, so let’s call it 10º to keep things simple.  Could be either.  And since it doesn’t really affect anything else in your structure as far as I can see, you can do whichever you want.  

I’d get a sliding bevel and set it at 1:6 for a splay of 9.4º, or if I really had my heart set on 10º, I’d set it with Rob’s drawing or with a slope of 3:17, magic numbers pulled out of the air (sorry) that give 10.01º.  And then I’d get busy with the fun of sawing Chris’ angled rabbets.  

I built an earlier version of Chris’ design a few years ago.  I enjoyed building it and use it a lot, plus it’s my favorite place to sit in the shop.

[Arlin Eastman]

Here are a couple of cheap ideas

https://www.amazon.com/GemRed-82305-Digi...uges&psc=1


Or one with out digital and just as good

http://www.eastwood.com/protractor.html?...oCJwjw_wcB

http://www.sears.com/uxcell-metal-15cm-1...Id=Everest Ventures&prdNo=7&blockNo=7&blockType=G7

[cputnam]

THIS plus a bevel angle gauge should solve your problem.

[Zhent]

Great thank you to everyone's comments. This will all come in very useful on this and future projects - the sawbench is the first thing that I'm putting together, and I'm running into many questions that I think don't often come up outside the most basic of beginners classes! It's great to have a place where I can ask even these relatively simple questions.

[Cooler]

If I were making this I would make a full-size plan upon which to lay the components and check for angles and dimensions.  

Regardless of the way you measure full sized plans will be an assistance.