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 \(m+n.\,\)

(第十二届AIME1994 第10题)