A circle has an arc of length 24π that is intercepted by a central angle of 80°.
What is the radius of the circle?
How to do I go about this?
+9479 arc length = radius * angle measured in radians
Convert 80º to radians.
80º * (π / 180º) rad. = 4π / 9 rad.
24π = radius * 4π / 9
54 = radius
+118667 A circle has an arc of length 24π that is intercepted by a central angle of 80°.
What is the radius of the circle?
The circumference of a circle is \(2\pi r\)
You have
\(\frac{80}{360} \text{ of the circle}\\ so\\ \frac{80}{360}*2\pi r = 24\pi\\ \frac{8}{36}*2 r = 24\\ \frac{4}{9}* r = 24\\ r = 24*\frac{9}{4}\\ r =54\;units\)
check
80/360*2*pi*54 = 75.3982236861550377
24*pi = 75.3982236861550377 
