Question

Find the measure of the central angle with a radius of 13 inches and the area of a sector measuring 42.25π square inches.



45°


90°


120°


180°

Answer 1

Area of a sector: 1/2r^2 theta

Need theta
Let x be theta for now

42.25 pi = 1/2r^2x
84.5pi = r^2x
84.5pi = 169x
x = 84.5pi/169 = roughly 1.57 in radians

Radians => degrees is 1.57 * 180/pi or roughly 90.