2006 AIME I Problem 14

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.)

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.