On a distant planet, a 20º central angle intercepts an arc of 4067 miles. What is the radius of the planet at its equator?

The radius of the planet is

miles. (Simplify your answer.)

Answer: 11,682.4 miles

Step-by-step explanation:

We can think the planet as a circle:

if we have a circle of radius R, and an arc of A degrees in the circle, the lenght of the arc is:

L = (A/180°) * 3.14*R

Here we know that:

L = 4076 miles

A = 20°

Then:

4076mi = (20/180) * 3.14*R = 0.3489*R

R = 4076mi/0.3489 = 11,682.4 miles