A central angle has a measure of 162 degrees and the intercepted arc's sector has an area measure of 84 cm², what is the radius of the circle?

Answer 1

Area = r^2(a)/2 = radius squared time half the angle (measured in radians)

84 = r^2(a)/2

168/a =r^2 162 degrees = 162pi/180 radians = 81pi/90 = 9pi/10

168/(9pi/10) =r^2

r^2 = 1680/9pi

r = sqr(1680/9pi)= about 13.7/pi = 13.7/3.14 = about 4.4 cm

radius = approximately 4.4 cm