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    Re: Angles without a protractor
    From: Don Seltzer
    Date: 2012 Oct 13, 10:02 -0700

    From: Sean C
    Date: 12 Oct 2012 04:29
    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!

    ----

    If you had marked the rays at 1 inch (or 1 foot or any arbitrary unit of measure) you would use a multiplier of 60.

    Mathematically, the reason this works is that for small angles, a good approximation is that an angle measured in radians is very nearly equal to its sine. To convert radians to degrees, multiply by 57.3. Mulitplying by 60 is close enough.

    For very small angles, the error will be nearly +5%. It declines to zero at about 60 degrees, and then goes negative, exceeding -5% at about 90 degrees.

    Don Seltzer
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