Problem of the Week 1106

Angle Measurement by Ruler

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Suppose you wish to measure the angle made by two lines, AB and AC, using a ruler alone.

Mark two points, X and Y, on AB and AC, respectively, so that the distances AX and AY are each m millimeters, m an integer. Measure the distance XY in millimeters and use that number to approximate (in degrees) the measure of angle BAC.

What should m be so that this approximation is best, in terms of minimizing the maximum error for angles of the form n degrees, where n ranges from 1 to 90?

Source: College Math Journal, "How to measure angles with a ruler," by Travis Kowalski, Sept 2008, pp. 273-279.

© Copyright 2008 Stan Wagon. Reproduced with permission.

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