2019 AMC 12A Problem 25

Let \triangle A_0B_0C_0 be a triangle whose angle measures are exactly 59.999^\circ, 60^\circ, and 60.001^\circ. For each positive integer n, define A_n to be the foot of the altitude from A_{n-1} to line B_{n-1}C_{n-1}. Likewise, define B_n to be the foot of the altitude from B_{n-1} to line A_{n-1}C_{n-1}, and C_n to be the foot of the altitude from C_{n-1} to line A_{n-1}B_{n-1}. What is the least positive integer n for which \triangle A_nB_nC_n is obtuse?

\textbf{(A) } 10 \qquad \textbf{(B) }11 \qquad \textbf{(C) } 13\qquad \textbf{(D) } 14 \qquad \textbf{(E) } 15

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