MathNet 2009-part-02 — 175 problems (EN–VI) Question 113

Let $M$ be the mid-point of the side $BC$ of a triangle $ABC$. Suppose $AB = 4$ and $AM = 1$, where by $XY$ we denote the length of the line segment $XY$. Determine the smallest possible value the angle $\angle BAC$ can take.