Question

An object moves exactly 45pi feet around a circle whose radius is 75 feet. Give the measure, in degrees and in radians, of the central angle that the object sweeps out.

Answer 1

Use the formula, S = r (theta), where

S = length of the arc of a circle
r = radius of the circle
theta = # of radians in the central angle of the circle

So substitute r = 75 and S = 45 pi

45 pi = 75(theta)

Divide both sides by 75

theta = 45 pi/75 or 3 pi/5

Therefore, there are 3 pi/5 radians in the central angle of the circle.

In degrees, 3pi/5 radians = 3(180)/5 = 108 degrees.

In degrees, 3 pi/5 is just 3(180)/5 =

Answer 2

Thank you so much

Answer 3

welcome. Hope that is very clear.

Answer 4

It is, Thanks