Question

What is the angle, in degrees, if the Area is 180 square miles and the radius is 42,240 feet?

Answer 1

Step-by-step explanation:

the area of a circle (all 360°) is

pi×r²

with r being the radius.

the area of a circle segment is just the corresponding fraction of the whole circle.

so the area of a segment of x degrees is

pi×r² × x/360

in our case we know

pi×42240² × x/360 = 180 mi²

we also know that there are 5280 ft in 1 mile.

so, the radius is actually

42240 / 5280 = 8 miles

and therefore our equation resulting in mi² has to use miles and not ft and has to look that way :

pi×8² × x/360 = 180 mi²

pi×64 × x/360 = 180

pi×64 × x = 180×360

pi×x = 180×360/64 = 1012.5

x = 1012.5/pi = 322.2887598...°

so, the angle of the segment of a circle with the area of 180 mi² and the radius of 8 mi is 322.2887598...°