Conic Sections · Challenge problem

Let $F_1$ and $F_2$ be the foci of the hyperbola $\dfrac{x^2}{16}-\dfrac{y^2}{9}=1$, and let $P$ be a point on its right branch with $\angle F_1PF_2 = 60^\circ$. Find the area of $\triangle F_1PF_2$.