numerical computation contest

[Jon Stratis]

Originally Posted by AGPapa

The arc is only one foot longer than the chord. How could the answer possibly be larger than one?

Create a simple approximation. Imagine a point C that lies at the top of the line H. You can then create a triangle ABC, where length AB is known (5280 ft) and length BC = AC = 5281/2 = 2640.5.

We know that h bisects line AB - lets call the intersection between AB and h to be H. we know that the length AH = BH = 5280/2 = 2640.

So, now we know two sides to the right triangle AHC - AH and AC. Taking the square of the hypotenuse minus the square of one side gives us the square of the other side. In other words, 2640.5^2 - 2640^2 = h^2 (the pythagorean theorem).

So, in this extremely rough approximation, we get h = 51.383. Given that, it's not hard to imagine that Christopher's answer could be correct, to some number of decimal places.