Forces and equilibrium — practice question

Particle $P$ has mass $0.3\,\mathrm{kg}$ and is joined to one end of a light inextensible string. The free end of the string is fixed at point $X$. A horizontal force of magnitude $F\,\mathrm{N}$ acts on the particle, and it is in equilibrium when the string makes an angle $\alpha$ with the vertical, where $\tan\alpha = \frac{8}{15}$ (see diagram).