Answer
$36.57^{\circ}$
Work Step by Step
First, using the fact that torque equals $\vec{r}\times\vec{F}$, we find that the y-component of the torque is 2.3 Newtons. Thus, the force's magnitude is:
$|F|=\sqrt{2.3^2+3.1^2}=3.86$
We simplify the equation for torque:
$\tau=rFsin\theta \\ \frac{\tau}{rF}=sin\theta \\ \theta = sin^{-1}(\frac{\tau}{rF})=sin^{-1}(\frac{4.6}{3.86\times2})=36.57^{\circ}$
