RO-TST 1988 Problem 14

Let $\Delta$ denote the set of all triangles in a plane. Consider the function $f: \Delta\to(0,\infty)$ defined by $f(ABC) = \min \left( \dfrac ba, \dfrac cb \right)$ , for any triangle $ABC$ with $BC=a\leq CA=b\leq AB = c$ . Find the set of values of $f$ .