This talk will start with the definition of the tangent cone (at a fixed point) of a subset of the Euclidean space. By letting ${}^{*}\mathbb{R}$ denote a non-standard model of the real field $\mathbb{R}$, a similar construction for subsets of ${}^{*}\mathbb{R}^{n}$ will be explored. Particularly, by seeing ${}^{*}\mathbb{R}$ as a real closed valued field, a useful formulation of the tangent cone of definable sets will be presented.