# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding

**Angles without a protractor**

**From:**Sean C

**Date:**2012 Oct 12, 04:29 -0700

Apologies if this has been mentioned before, but I just learned a method for drawing/measuring angles using only a ruler. Thought some here might be interested.

It turns out that if you have an angle you want to measure, you can mark each of its rays at 3 inches, measure the distance between the two points, multiply the result (in decimal inches) by 20 et voila!

I used the following method to draw an angle of 35°: I drew a roughly horizontal line on a piece of paper and marked it 3" from one end. I then constructed an arc by measuring and marking a few points, all at 3" from the same end. Next, I measured a secant line with a length of 1.75" (35/20) within the arc with one end at the first 3" mark I made on the horizontal line. I marked the other end and connected the vertex with this point.

Upon measuring the angle with a protractor I found it to be 34°. Not perfect, but would probably do in an emergency. And if I had spent more than a couple seconds marking it out, I may have achieved better accuracy, IDK. Of course there are other methods to achieve the same result. Anyway, someone who knows much more about math than I do figured out that the maximum error should be about 6% for a 90° angle. Again, IDK if that's correct.

As far as I can tell, the method will work for any unit of measurement. Hope someone finds this mildly interesting, if not useful. :)

Cheers,

Sean C

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