If the measurement of a central angle is 5 pie /6 , find the length of its intercepted arc in a circle with a radius of 15 inches.

There are several information's already given in the question. Based on those information's the answer to the question can be easily determined. Now let us focus on the problem in hand.

Measure of the central angle = 5 pie / 6
Radius = 15 inches
Value of pie = 3.14
Then
Arc length = Measure of central angle * Radius
                 = [(5 * 3.14)/6] * 15
                 = (15.7/6) * 15
                 = 39.25 inches
I hope the above procedure is clear for you to understand.