MathDB

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

Problem Statement