Trigonometry · Superchallenge problem

At a certain moment, a $1.5$-metre post standing on level ground casts a $2$-metre shadow. At the same moment, a $12$-metre vertical pole stands on a hillside that slopes straight down, directly away from the sun, at an angle $\alpha$ below the horizontal with $\tan\alpha = \dfrac{5}{12}$. Find the length of the pole's shadow, measured along the hillside, in metres.