Question

Find the arc-length of a circle with the given radius r and central angle 0. Give the answer in the given unit of measure, rounded to the nearesthundredthr = 20 km: 0 = 240°

Answer 1

The length of the arc of a circle whose radius is r and the angle of the arc is cita is

$L=r\theta$

Where cita is in the radian measure

Since r = 20 km

Since cita = 240 degrees

Change at first the measurement of the angle to radian by multiplying the degree measure by pi/180

$\begin{gathered} \theta=240\times\frac{\pi}{180} \\ \theta=\frac{4}{3}\pi \end{gathered}$

Substitute them in the rule above to find the length of the arc

$\begin{gathered} L=20\times\frac{4}{3}\pi \\ L=83.7758041 \end{gathered}$

Round it to the nearest hundredth

L = 83.78 km

The length of the arc is 83.78 km