The easiest way to relate the length of an arc and its radius uses radian units rather than degrees. A 1-radian angle is one whose radius equals its length. After your calculation, however, you can convert your result to degrees. To calculate using inches when one measurement uses another unit, add one more conversion step by changing centimeters to inches.
Multiply the arc's radius, measured in centimeters, by 0.394 to convert it to inches. If the radius equals 4 cm, 4 x 0.394 = 1.58 inches.
Divide the arc length, measured in inches, by your answer. If the arc measures 1.2 inches: 1.2 / 1.58 = 0.76. This answer is the arc size, measured in radians.
Multiply your answer by 57.3 to convert to degrees. One radian equals 57.3 degrees, which equals 180 divided by pi. 0.76 x 57.3 = 43.5 degrees.
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