In the September 2008 issue of the *College Mathematics Journal* Travis Kowalski presents an neat way to measure an angle using a ruler. He attributes the discovery to a student of his, Tor Bertin.

Given an acute angle (the technique can be modified for obtuse angles), measure off a distance on each ray. Then measure the distance between these two points, . He claims that is approximately degrees.

He illustrated this technique using . Some example include:

- if , then the approximation is
- if , then the approximation is
- if then the approximation is
- obviously, if , then the approximation is .

As another example, if we take to be 6 centimeters, then the measurement of in milimeters is the approximate number of degrees for .

The derivation of this approximation is elementary. Using trigonometry, it is easy to see that . Assuming sine takes angles in radians, but that is measured in degrees, this becomes . Then the fact that and yields the desired result.

The rest of the article is devoted to looking at whether 60 is the best constant to be used in this approximation formula.

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