Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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Which function is used to calculate the angular measurement in degrees for arc length?

Arc Length = s = rθ
Arc Length = s = πrθ
Arc Length = s = πrθ/180
Arc Length = s = θr²/2

The correct answer is: Arc Length = s = πrθ/180

The function used to calculate the angular measurement in degrees for arc length can be derived from the relationship between arc length, radius, and the angle in degrees. The formula for arc length is generally given by the equation $ s = rθ $ when the angle $ θ $ is measured in radians. However, when the angle is expressed in degrees, a conversion factor is needed. In the correct answer, the formula $ s = \frac{πrθ}{180} $ incorporates this conversion factor. The reasoning is that there are 180 degrees in π radians, so to convert degrees into radians, you multiply the degree measure by $ \frac{π}{180} $. This modulates the original formula to appropriately calculate the arc length based on the angle provided in degrees. Thus, when using this formula, you can accurately determine the arc length for any circle given the radius and the angle measured in degrees.