2006 AIME I Problems/Problem 14
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Problem
A tripod has three legs each of length 5 feet. When the tripod is set up, the angle between any pair of legs is equal to the angle between any other pair, and the top of the tripod is 4 feet from the ground In setting up the tripod, the lower 1 foot of one leg breaks off. Let 
be the height in feet of the top of the tripod from the ground when the broken tripod is set up. Then can be written in the form 
where 
and 
are positive integers and is not divisible by the square of any prime. Find 
(The notation 
denotes the greatest integer that is less than or equal to 
)
Solution
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