From the right triangle made of the observer, the planet center and the "horizon" on the surfac (where the right angle is), we find $$ \sin \alpha = \frac r{r+d}$$ where $\alpha=3^\circ$ is the observed angle, $d=100{,}000\,\text{mi}$ (or nm?) is the observed distance. Solving for $r$, we find $$ r = \frac{d\sin\alpha}{1-\sin\alpha}$$ Your pocket calculator should be able to evaluate this (to check your computation: the result looks like $x{,}xxx.x276\ldots\,\text{mi}$)