Answer
The direction of $\vec{d}_{B}$ is
$$\theta_{B}=48^{\circ}$$
Work Step by Step
The direction of $\vec{d}_{B}$ is
$$\theta_{B}=\tan ^{-1}\left(\frac{d_{B, y}}{d_{B, x}}\right)=\tan ^{-1}\left(\frac{3 / 2+\sqrt{3}}{2+\sqrt{3} / 2}\right)=\tan ^{-1}(1.13)=48^{\circ}$$
