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. 330° 12 ft 5.8 ft 6.3 ft 27.5 ft 69.1 ft

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ 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 formula $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$. Given $\theta_{deg}=330^{\circ}$, then $\theta_{rad}=\frac{\pi}{180}\times330=\frac{11\pi}{6}$ radians, and $r = 12$ ft.

Step2: Substitute values into arc - length formula

Substitute $r = 12$ and $\theta=\frac{11\pi}{6}$ into the arc - length formula $s=r\theta$. So $s=12\times\frac{11\pi}{6}$.

Step3: Simplify the expression

$12\times\frac{11\pi}{6}=2\times11\pi = 22\pi$.

Step4: Approximate the value

Since $\pi\approx3.14$, then $s\approx22\times3.14=69.08$ ft.

Step5: Round to the nearest tenth

Rounding $69.08$ to the nearest tenth gives $s\approx69.1$ ft.

Answer:

69.1 ft