What is the max height a boeing 747 can fly, under the St. Louis Arch?

What's the max height a Boeing 747 plane can fly, through the Gateway arch in Saint Louis? Without clipping its wings/tail.What is the max height a boeing 747 can fly, under the St. Louis Arch?
Max altitude is 589 feet, limited by the wing span. At that altitude there is still 104.6 feet of

overhead clearance so the tail will be safe.



The equation of the arch is:



y = 693.8597 - 68.7672 cosh ( 0.0100333 x )



where y = height, x = distance from the center of the base.



Just set x = wingspan/2 and compare the y value to maximum height.



Of course this assumes the arch is an infinitely thin mathematical curve. If I were flying the

plane I'd get up a little higher to allow for the thickness of the arch.



This URL gives the equation of the arch (sorry to split it up, but Yahoo may try to truncate

it if I don't)



http://www4.carthage.edu/faculty/cchell/鈥?/a>

CalcIIs05.Gateway%20Arch.htm
http://en.wikipedia.org/wiki/Gateway_Arc鈥?/a>



Go for it... here's the link to wolfram alpha if you need it:

http://www.wolframalpha.com/



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By the way, I've seen this problem before on Y!A. I expect you're told to assume it's a parabola (it's an untrue assumption, but it makes it easier). I find it extremely odd that you would omit information you're told in the problem...What is the max height a boeing 747 can fly, under the St. Louis Arch?
I think we need to know the mathematical function that defines the inner boundary of the arch.