Question

Arc Length S. Central Angle 0 82 miles. 135°Find the radius and radians r of a circle with an arc length s and a central angle 0.

Answer 1

Central angle of 135 degrees = 135 (Pi/180) = (3/4)Pi = 2.356 radians

First answer:

Central angle = 2.356 radians

Arc lenght = 2 Pi r (angle/360), in this case:

82 = 2 Pi r (135/360) = 2 Pi r (3/8) = (3/4) Pi r

82 = (3/4) Pi r

r = 82/(3/4)Pi = 82/2.35619449

r = 34.80188089

Second answer:

Radius = 34.8 miles