1994 AIME Problem 10

In triangle ABC,\, angle C is a right angle and the altitude from C\, meets \overline{AB}\, at D.\, The lengths of the sides of \triangle ABC\, are integers, BD=29^3,\, and \cos B=m/n\,, where m\, and n\, are relatively prime positive integers. Find m+n.\,

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.