Since the forces are in equilibrium, the sum of the horizontal and vertical components must be zero.

Resolving horizontally:

\(P \cos 25^\circ = 22 + 16 \cos 55^\circ\)

Resolving vertically:

\(Q + 16 \sin 55^\circ = P \sin 25^\circ\)

First, solve the horizontal equation for \(P\):

\(P = \frac{22 + 16 \cos 55^\circ}{\cos 25^\circ}\)

Substitute \(P\) into the vertical equation:

\(Q + 16 \sin 55^\circ = \left(\frac{22 + 16 \cos 55^\circ}{\cos 25^\circ}\right) \sin 25^\circ\)

Solve for \(Q\):

\(Q = \left(\frac{22 + 16 \cos 55^\circ}{\cos 25^\circ}\right) \sin 25^\circ - 16 \sin 55^\circ\)

Calculating these values gives:

\(P \approx 34.4\)

\(Q \approx 1.43\)