Question

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

Answer 1

Answer: d. 39.3 inches

Step-by-step explanation:

Given the measurement of central angle ( $\frac{5\pi}{6}$ ) and the measure of radius (15 inches), the lenght of the intercepted arc in the circle can be calculated with the formula:

$arc\ length=r\theta$

Where r represents the radius of the circle and $\theta$ the central angle.

Substituting $\theta=\frac{5\pi}{6}$ and $r=15inches$ into the formula $arc\ length=r\theta$:

$arc\ length=(15inches)(\frac{5\pi}{6})\\arc\ length=39.3inches$