Question

circle p has a radius of 50 yards. major arc rst on the circle has a central angle of 215°. what is the length of major arc rst? select the correct answer. 130π yards 140π yards $\frac{1075}{18}pi$ yards $\frac{1075}{9}pi$ yards

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc of a circle is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius of the circle, and $\theta$ is the central angle in radians. First, convert the central angle from degrees to radians. The conversion formula is $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$. Given $\theta_{deg}=215^{\circ}$, then $\theta=\frac{215\pi}{180}=\frac{43\pi}{36}$ radians, and $r = 50$ yards.

Step2: Calculate arc - length

Substitute $r = 50$ and $\theta=\frac{43\pi}{36}$ into the arc - length formula $s=r\theta$. So $s = 50\times\frac{43\pi}{36}=\frac{2150\pi}{36}=\frac{1075\pi}{18}$ yards.

Answer:

$\frac{1075\pi}{18}$ yards