We consider the collapse of a saddle of a horseshoe and a sink via a critical saddle-node bifurcation. In this way one obtains a saddle-node horseshoe. We prove that there is an open set of arcs of diffeomorphisms \{f_\mu\}_{\mu \in I} unfolding generically, say at \mu_0, a saddle-node horseshoe with Hausdorff dimension arbitrarily close to 1/2 so that there is an interval (\mu_0, \mu_0+\varepsilon) in the parameter line such that every diffeomorphism f_\mu, \mu\in (\mu_0, \mu_0+\delta), has a tangency.