  In this paper, we study the angle estimate of distance functions from minimal
hypersurfaces in manifolds of Ricci curvature bounded from below using
Colding's method in [13]. With Cheeger-Colding theory, we obtain the Laplacian
comparison for limits of distance functions from minimal hypersurfaces in the
version of Ricci limit space. As an application, if a sequence of minimal
hypersurfaces converges to a metric cone $CY\times\mathbb{R}^{n-k}(2\leq k\leq
n)$ in a non-collapsing metric cone $CX\times\mathbb{R}^{n-k}$ obtained from
ambient manifolds of almost nonnegative Ricci curvature, then we can prove a
Frankel property for the cross section $Y$ of $CY$. Namely, $Y$ has only one
connected component in $X$.
