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 $$h$$ be the height in feet of the top of the tripod from the ground when the broken tripod is set up. Then $$h$$ can be written in the form $$\frac m{\sqrt{n}},$$ where $$m$$ and $$n$$ are positive integers and $$n$$ is not divisible by the square of any prime. Find $$\lfloor m+\sqrt{n}\rfloor.$$ (The notation $$\lfloor x\rfloor$$ denotes the greatest integer that is less than or equal to $$x.$$)

(第二十四届AIME1 2006 第14题)