A particle $P$ has weight $10{\text{ }}N$ and is in limiting equilibrium on a rough horizontal table. The forces shown in the diagram represent the weight of $P$, an applied force of magnitude $4{\text{ }}N$ acting on $P$ in a direction at ${30^ \circ }$ above the horizontal, and the contact force exerted on $P$ by the table (the resultant of the frictional and normal components) of magnitude $C{\text{ }}N$.
a) Find the value of $C$.
b) Find the coefficient of friction between $P$ and the table.

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