find the EXACT length of an arc that subtends a central angle of 80 degrees in a circle of radius 4 meters

Question

find the EXACT length of an arc that subtends a central angle of 80 degrees in a circle of radius 4 meters.

find the EXACT length of an arc that subtends a central angle of 80 degrees in a circle of radius 4 meters

Thanks!

Answer 1

Hello Danny,

For context, the length S of an arc that subtends a central angle of theta in radians in a circle of radius r is given by S = r*(theta).

For this problem, r = 4 meters, and theta = 80 degrees, which converts to 80*(pi/180) radians, or 4/9 pi radians.

So, the arc length S = 4*(4/9 pi) = 16/9 pi meters.

Hope this helps!