$$\require{cancel}$$
Thumbnails: If $$C$$ is acute, then $$A$$ and $$B$$ are also acute. Since $$A \le C$$, imagine that $$A$$ is in standard position in the $$xy$$-coordinate plane and that we rotate the terminal side of $$A$$ counterclockwise to the terminal side of the larger angle $$C$$. If we pick points $$(x_{1},y_{1})$$ and $$(x_{2},y_{2})$$ on the terminal sides of $$A$$ and $$C$$, respectively, so that their distance to the origin is the same number $$r$$, then we see from the picture that $$y_{1} \le y_{2}$$. Image constructed by Michael Corral (Schoolcraft College).