Earlier quoted context omitted.
It seems like one of those stupid brain teasers tech companies used to ask that are not very correlated with success but act as arbitrary filters.
I don't see anything tricky about that problem. It requires some junior high geometry and high school trig, and yes, I suppose you need to know the radius of the earth offhand. Still. That strikes me a lot more as a math fizzbuzz than as a brain teaser. A college applicant can be reasonably expected to know this stuff.
Or you can easily derive the radius if you remember that a meter was initially defined as 1/10,000,000 of the distance from the equator to the North Pole. So you can easily calculate the Earth's circumference, and from there the radius: 10,000,000 * 4 / 1000 / 3.1416 / 2 = 6366 km.
Wikipedia gives 6371 km as the mean radius.