Question

what is the approximate length of arc s on the circle below? use 3.14 for π. round your answer to the nearest tenth. 135° 6 in. 14.1 in.

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central - angle in radians. First, convert the angle from degrees to radians. We know that to convert degrees to radians, we use the conversion factor $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg}=135^{\circ}$, then $\theta_{rad}=135\times\frac{\pi}{180}=\frac{3\pi}{4}$ radians, and $r = 6$ inches.

Step2: Substitute values into the arc - length formula

Substitute $r = 6$ and $\theta=\frac{3\pi}{4}$ into the formula $s=r\theta$. So $s=6\times\frac{3\pi}{4}=\frac{18\pi}{4}=\frac{9\pi}{2}$.

Step3: Approximate the value

Since $\pi\approx3.14$, then $s=\frac{9\times3.14}{2}=\frac{28.26}{2}=14.13$.

Step4: Round to the nearest tenth

Rounding $14.13$ to the nearest tenth gives $14.1$.

Answer:

$14.1$ in.