Problem

Figure 3

Figure 3 shows two horizontal forces $P$ and $Q$ acting on a particle.

The angle between the direction of $P$ and the direction of $Q$ is $150^\circ$

Force $P$ has magnitude $X$ newtons.

Force $Q$ has magnitude $5\sqrt{3}\text{ N}$.

The resultant of $P$ and $Q$ has magnitude $\sqrt{129}\text{ N}$.

Find

(i) the value of $X$,

(ii) the angle between $Q$ and the resultant, giving your answer to the nearest degree.