A particle P of mass 0.3 kg is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point X. A horizontal force of magnitude F N is applied to the particle, which is in equilibrium when the string is at an angle α to the vertical, where \(\tan \alpha = \frac{8}{15}\) (see diagram). Find the tension in the string and the value of F.