# another geometry question



## sunnybob (15 Sep 2019)

I need to lay out a template drawing, about 2 ft square.
One of the angles in the drawing is 5 degrees past 90.
I have some very basic plastic protractors.
I have a mitre saw, but there is no stop at 5 degrees.
I have a reasonably good mitre fence for the bandsaw / router table / table saw. 

But at that small an angle its all about how good I can guess the lines, and it seems I'm not such a good guesser.
Is there a way to calculate that 5 degree line, so I can just use a compass / rule / or something as basic?
It needs to accurate to within a fine pencil line over a 20 " distance.


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## Trevanion (15 Sep 2019)

Measure 44.5mm across, 508mm (20") up. Perfect 5-degree angle.


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## sunnybob (15 Sep 2019)

Thank you. I'm not going to ask how that works because I KNOW my brain will hurt.
:roll: =D> =D>


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## sploo (16 Oct 2019)

For the brain-hurting:

arctan(44.5/508) ~= 5 degrees

Working backwards, if you measure _n_mm up and want an angle of _a_ degrees then you need to go _w_mm across, where:

w = n * tan(a)

E.g. 200mm up with a 10 degree angle is 200 * tan(10) = 35.3mm across.

PS Note that some calculators may default to angles in radians (RAD). Make sure it's set to DEG if you want to use degrees.
PPS arctan is sometimes shown as tan-1


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## sunnybob (16 Oct 2019)

sploo, fully understood :roll: :roll: :roll:


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## sploo (16 Oct 2019)

sunnybob":2ywx32c5 said:


> sploo, fully understood :roll: :roll: :roll:


 :mrgreen:


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## Jacob (17 Oct 2019)

Or if you want to just have a stab at it: as near as you can; draw a right angle (=90º), divide it into 3 equal angles (=30º), divide one of these into 3 (=10º), divide that into 2 (=5º)
Graphical setting out and calculating, using dividers, straight edges, projections etc tends to get very over looked. May be less precise but may be more accurate i.e. nearer the mark than getting the maths hopelessly wrong, and good enough for woodwork.
n.b. 30º is the woodworkers basic angle - for sharpening for starters and for a lot of other things. Worth practicing to hit it visually from memory. (Don't do it with your arm in the air or people might think you are a brexit supporter!)


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## AndyT (17 Oct 2019)

I'm no mathematician but I thought I'd read that dividing an angle into three is not possible with ruler and compasses. Wikipedia says that's true, except for a few special cases, including 90°.

https://en.m.wikipedia.org/wiki/Angle_trisection

So you can get to 30° but getting to 5° is going to need some approximation.

No big deal - and using trig depends on approximation too, for the accuracy of the measurements.


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## Jacob (17 Oct 2019)

AndyT":2umrkdmb said:


> I'm no mathematician but I thought I'd read that dividing an angle into three is not possible with ruler and compasses. Wikipedia says that's true, except for a few special cases, including 90°.
> 
> https://en.m.wikipedia.org/wiki/Angle_trisection
> 
> So you can get to 30° but getting to 5° is going to need some approximation.


Yes. 
I might have a bash and see how close. I'd bet on less than 1 º error.

PS dunnit! That didn't take long about 30 seconds. Took longer to find protractor to check it with.
Started with 90º (corner of page). Drew the lines with straightedge just guessing by eye. Got to just over 4.5º
PPS it's possible to construct 30º accurately with straight edge and dividers (equilateral triangle and bisected angle)) so that could be more accurate than starting with 90º and just eyeballing.


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## sunnybob (17 Oct 2019)

You lot DO realise this thread is over a month old, and I had actually forgotten why I asked the question? :roll: :roll: 
(it was to make the legs for the coffee table)

But if you want to play amongst yourselves untill my next brain squeezer comes along, i'm fine with that. =D> =D> =D> =D> =D>


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## Jacob (17 Oct 2019)

:lol: 
Hadn't noticed. Maybe it took sploo a month to work out how to do it!
PS Just had another look - it's possible to construct 15º with straightedge and compasses so the only eyeballing would be the final division into 3 x 5º
My faith in Euclid grows by the minute!
Seriously though - it took me a long time to work out why on earth they taught us this sort of very useful geometry at school (no pun intended :roll: )


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## sunnybob (17 Oct 2019)

my school was an inner London secondary modern, HEAVY accent on the secondary. :roll: 

we barely got through decimals and had just started algebra before I left to earn a living. 8)


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## Jacob (17 Oct 2019)

sunnybob":3kps7ikb said:


> my school was an inner London secondary modern, HEAVY accent on the secondary. :roll:
> 
> we barely got through decimals and had just started algebra before I left to earn a living. 8)


Geometry is easier and was usually taught early on because it was essential for people making things and for other practical apps. There's a lot of it in older woodwork teaching books. Still is essential!


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