Calculus · Easy problem

A $13$-foot ladder leans against a wall; the angle its base makes from the vertical wall is $\theta(x)=\arccos\!\left(\dfrac{x}{13}\right)$, where $x$ is the horizontal distance of the foot from the wall. A safety sensor halts the ladder once this angle is changing at exactly $-\dfrac{1}{12}$ rad per foot. Find the distance $x$ at which this happens.