Question

Find the length of the arc on a circle with the radius of 2.4 km and is intercepted by a central angle measuring 150°. Leave your answer in terms of pi

Answer 1

Formula to find the arc length is:

$s=\frac{\theta}{360} 2\pi r$

Where, s= arc length,

r = radius of the circle

\theta = central angle in degrees.

According to the given problem, \theta= 150 and r =2.4.

So, first step is to plug in these values in the above formula to get the arc length.

$s=\frac{150}{360} *2\pi *2.4$

=$\frac{5}{12} *2\pi *2.4$

$=0.41667*2\pi *2.4$

$=2\pi$

So, arc length is $2\pi$.