The sides of a triangle are of lengths $13$, $14$, and $15$. The altitudes of the triangle meet at point $H$. if $AD$ is the altitude to the side of length $14$, the ratio $HD:HA$ is:
$\textbf{(A) }3:11\qquad\textbf{(B) }5:11\qquad\textbf{(C) }1:2\qquad\textbf{(D) }2:3\qquad \textbf{(E) }25:33$
Using Law of Cosines
and the fact that the ratio equals cos(a)/[cos(b)cos(c)]
B 5:11