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(Distance)2 = (6)2 + (8)2 = 36 + 64 = 100

Distance = sqrt(100) = 10 miles

To be honest about it, this is only an approximation. The formula used here is only valid

on a flat surface, and we all know that the earth is a spherical surface.

Even worse than that ... the formula is only valid if the two directions are perpendicular (90°)

to each other. But north and east are only perpendicular at the equator; the farther you are

from the equator, the less perpendicular they are.

To show you how bad it can get: If you start at the north pole, go 6 miles south,

and then go 8 miles east, you wind up only 6 miles from where you started.

In order to answer this question accurately, you have to know exactly where on earth

the marathon runner started from, and then you have to use spherical trigonometry.

I'm sure you'll be happy that I'm not going to do that. It's valid because we don't know

where he started from.

We'll just say: The answer is "approximately 10 miles", and the closer our runner is

to the equator, the more accurate this answer is.

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Q: A marathon runner runs 6 miles south and then 8 miles east How far is the runner from the starting point?
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