The correct answer is $\boxed{\text{B}}$.
The angle between two vectors can be calculated using the following formula:
$$\cos \theta = \frac{\mathbf{u} \cdot \mathbf{v}}{|\mathbf{u}||\mathbf{v}|}$$
where $\mathbf{u}$ and $\mathbf{v}$ are the two vectors, and $\theta$ is the angle between them.
In this case, the vectors are $\mathbf{u} = (0.866, 0.500, 0)$ and $\mathbf{v} = (0.259, 0.966, 0)$. Substituting these values into the formula, we get:
$$\cos \theta = \frac{(0.866)(0.259) + (0.500)(0.966) + (0)(0)}{|(0.866, 0.500, 0)| |(0.259, 0.966, 0)|} = 0.7071067811865475$$
Taking the arccosine of both sides, we get:
$$\theta = \arccos 0.7071067811865475 = 45^\circ$$
Therefore, the angle between the two vectors is $\boxed{45^\circ}$.
The other options are incorrect because they do not correspond to the angle between the two vectors.