# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Angles without a protractor**

**From:**Lu Abel

**Date:**2012 Oct 12, 14:46 -0700

Whoops, meant to say "chord" in item (c). Secant is a rather inexact term, except as the trigonometric value of the reciprocal of the cosine of an angle.

From:Lu Abel <luabel{at}ymail.com>

To:"NavList@fer3.com" <NavList@fer3.com>

Sent:Friday, October 12, 2012 2:37 PM

Subject:[NavList] Re: Angles without a protractor

Because you are measuring the chord of an angle and not around the arc, the angle calculated by this method is

a) a bit greater than it actually is for angles less than 60 degrees (zero error, of course, at zero degrees, then increases and then decreases as angle grows)

b) exact at 60 degrees -- an equilateral triangle has a chord of exactly the length of its two radii

c) rapidly degenerates beyond that For example, the secant of 90 degree angle is the hypotenuse of a equal-sided right triangle. If the sides are 3" per the rule, the measured hypotenuse would be 4.24 inches, leading one to believe the angle was 85 degrees.

From:Robert Bernecky <bernecky---.net>

To:NavList@fer3.com

Sent:Friday, October 12, 2012 12:23 PM

Subject:[NavList] Re: Angles without a protractor

You said …drew an angle of 35°… I found it to be 34°…Out of curiosity, I was interested in the error in this simple approach. As you can see from the curve given in the attachment, you found exactly what you should have.Attached is a curve giving the correction to be applied to your calculated angle.

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