Draw Me an Angle Using Just a Ruler

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Forum topic by Kelly posted 02-04-2015 03:55 AM 3079 views 0 times favorited 113 replies Add to Favorites Watch
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2039 posts in 2973 days

02-04-2015 03:55 AM

Topic tags/keywords: angles formulas procedure technique find an angle draw an angle tip

I needed some angle cuts that extended well past the limits of most protractors. I haven’t been in school for more than forty years and never took geometry or any other class beyond basic math. As such, playing with complex formulas or compasses (which are mostly small and no less limited than protractors) was not something I was wont to do. No doubt, many others are like me in that fact.

All these things said, I came up with a means of, very accurately, finding any angle. It does involve several steps, but my digital and other protractors indicated I was quite close in my measurements. In truth, I believe any inaccuracies were in projecting the line of the short (no longer than 12”) protractors, rather than my calculations/methods.

I will share the approach, of course, but I’d like to see how others got there, or would get there using just a ruler and a bit of mathematical rambling, at basic levels. I will say using pi is fair, though I did not. Again, I used only a ruler. Anyone want to weight in?

113 replies so far

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#1 posted 02-04-2015 04:37 AM


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#2 posted 02-04-2015 04:50 AM

snap a chalk line


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#3 posted 02-04-2015 04:51 AM

Pi r squared

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#4 posted 02-04-2015 05:44 AM

jtm, what does that mean? Remember, we’re trying to draw an angle with nothing more than a ruler and BASIC math at our disposal.

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2039 posts in 2973 days

#5 posted 02-04-2015 05:47 AM

Pi x r 2’d, isn’t that the formula for circumference, or area, or rocket fuel? I need to draw an angle.

We can use the ruler/yard stick/tape and the 3-4-5 formula to start by drawing a ninety degree triangle.

Took me a moment to realize I’d finally seen the end of computing pi…...............

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2039 posts in 2973 days

#6 posted 02-04-2015 05:48 AM

To be clear, I’m looking for an angle, such as twenty degrees and it needs to be within a degree.

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#7 posted 02-04-2015 07:31 AM

I’m curious…

If a protractor is 180 degrees, how could you ever exceed its capability?

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#8 posted 02-04-2015 08:22 AM

4 cubits / 11 cubits

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#9 posted 02-04-2015 09:11 AM

I’m intrigued, and also horrible with most math type calculation scenarios, so I’d really like to see exactly what you’re referring to.

-- Richard, Hot Springs, Ar -- Galoot In Training

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#10 posted 02-04-2015 10:14 AM

Kelly, can be done but need to know, width, length constraints.
Are you needing to cut an angle from the end of narrow board or across a larger panel?

-- Sawdust and shavings are therapeutic

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#11 posted 02-04-2015 11:35 AM

I started with a ninety degree angle, since it was the easiest to come by. All I had to do was use an L square, or measure 3,4 then 5 feet (measure three feet, turn, measure four feet, turn the same way and line the tape with where I started).

Once I had a ninety degree angle, I could get started, or go equal distance on each leg, measure the distance between the two points and split it in half for forty-five degrees.

Depending on how big the item was going to be, I could use eighth of an inch, quarters of an inch, halves or even larger fractions or whole numbers to represent each degree mark.

We know the entire angle is ninety degrees, so, if we use the ninety degree angle, we will need to use ninety of the chosen increments. If we used the forty-five degree angle, it would, of course, require we use forty-five of them.

Staying with the forty-five degree angle and choosing 1/8” increments, I will need a measurement 45/8th’s, (5”5/8”), which will be measured across the angle from two points that are an equal distance up the two legs of the 45.

It may take a couple runs, moving the line between the two legs up or down them, before you find the position which gives you your 5-5/8” distance.

Once you find the points that will give you the 5-5/8” distance, you can double it, rather than resort to trial and error again. You could also make a chart, which I will, giving the measurements for extended points.

With your line ran between the two legs, mark eight inch increments on it for the forty-five degree marks. Mark critical positions, such as 90, 72, 60, 45, 30 and 22-1/2 degrees for easy location in the future.

Using this, you can mark any angle accurately. You can, then, use Paul’s chalk line to mark your angle.

I found this useful for setting up to run 2x’s for ten degree angle cuts.

and working in the area I know the angle will be, eventually, drawn,

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#12 posted 02-04-2015 01:08 PM


- jtm

I’ve heard the lengthy story about the indian chief Soh Cah Toa… but I’ve also heard that back in the 60’s “Some Old Hippy Caught Another Hippy Tripping On Acid”. Got any other fun ones?

Anyways, the answer is to expand beyond basic math and use trigonometry. Even if you don’t learn it there are online calculators that take the learning out of the equation (heh).

Punch in two values you know such as angle A as 20 degrees and side b as 10 (units don’t matter, interpret them all as the same). The result is that you get side a as a length of 3-5/8”. This will get you as accurate as you can measure 90deg and straight lengths. Oh, you can use this to make a big 90 as well. Put in 120” for both sides a and b and the diagonal (hypotenuse) is 169.71”. Even if you round to 169-3/4” you would only be off by 0.015degree so it’s pretty easy to get fairly accurate.

Also, I think that your method won’t be right. You are taking a straight line and dividing it into equal segments? You need to take a circle and divide it’s circumference into equal segments to get equal angles between each point.

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#13 posted 02-04-2015 01:38 PM

School Closed Today…..... Oscar Had A Hit Of Acid

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#14 posted 02-04-2015 01:44 PM

The reason your method won’t work is because the same reason it does work for a 45. For the 45 your distance on both legs are the same, but if you try to use the original line with 90 segments to find a different angle it would be like using different lengths for each leg and that is what throws it off.

-- Because I'm gone, that's why!

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#15 posted 02-04-2015 01:56 PM

-- Perform A Random Act Of Kindness Today ... Pay It Forward

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