Question 72
Let $ABC$ be a triangle right-angled at $A$, with $\angle ABC = 15^\circ$. Let $H$ be the foot of the altitude from $A$ and let $J, K$ be the projections of $H$ onto $AB$ and onto $AC$. Knowing that the area of $AJHK$ is $45~\mathrm{cm}^2$, how many $\mathrm{cm}^2$ is the product $BJ \cdot CK$?