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**HallsofIvy** 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 $\displaystyle 140\pi= 438$ miles and you could drive around the earth in about 6 hours!

The "equation for arclength is $\displaystyle S= r\theta$" **only** if [itex]\theta[/itex] is given in **radians**! So you need to start writing the angle in radians. 180 degrees corresponds to $\displaystyle \pi$ radians so $\displaystyle 1.4333^o$ degrees corresponds to $\displaystyle 1.4333/180= 0.0079611\pi= 0.025016$ 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 $\displaystyle 360^o$ covers the entire circumference, $\displaystyle 2\pi r$ and angle of $\displaystyle 1.4333^o$ covers $\displaystyle \frac{1.4333}{360}(2\pi r)$ of the circumference. So we have $\displaystyle \frac{1.4333}{360}(2\pi r)= 100$ 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 $\displaystyle r= \frac{100}{0.0250156}= 3997$ miles, again.