Question

find the length of arc abc. use 3.14 for the value of π. 17 cm 120° round to the nearest hundredth of a cm.

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 $120^{\circ}=120\times\frac{\pi}{180}=\frac{2\pi}{3}$ radians, and $r = 17$ cm.

Step2: Calculate the arc - length

Substitute $r = 17$ cm and $\theta=\frac{2\pi}{3}$ into the arc - length formula $s=r\theta$. So $s = 17\times\frac{2\pi}{3}$. Using $\pi = 3.14$, we have $s=\frac{17\times2\times3.14}{3}=\frac{106.76}{3}\approx35.59$ cm.

Answer:

$35.59$ cm