Math CentralQuandaries & Queries


Question from Deb, a student:

How do I find the degree measure of an arc in a circle with the Length of 14 and the radius of 70?

Hi Deb,

The circumference of a circle of radius 70 units is $2 \pi r = 2 \pi \times 70 = 439.82$ units. Your arc is only a fraction of the circle, in fact the length of your arc is $\large \frac{14}{439.82}$ of the circumference of the circle. By the symmetry of the circle the angle of the arc is $\large \frac{14}{439.82}$ of the angle of the entire circle, which is 360o. What is the measure of this angle?


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