Unfortunately, purebladeknight's argument is incorrect. The radius of the earth is considerably larger than 3000/43= 70 miles. If it were that radius, the circumference of the earth would be

miles and you could drive around the earth in about 6 hours!

The "equation for arclength is

"

**only** if [itex]\theta[/itex] is given in

**radians**! So you need to start writing the angle in radians. 180 degrees corresponds to

radians so

degrees corresponds to

radians.

And a radian is

**defined** so 1 radian cuts an arc equal to the radius. Here the arc is 100 miles= 0.025016 times the radius of the earth so the earth's radius is 100/0.025016= 3997 miles, approximately.

If you wanted to do this in degrees, you could argue by proportions. An entire arc of

covers the entire circumference,

and angle of

covers

of the circumference. So we have

to solve for r. The first thing you would do, of course, if find that coefficient: [tex]\frac{1.4333}{360}(2\pi)= 0.025016[tex] (the radian measure we got before). Now your equation is 0.0250156 r= 100 so

miles, again.