To solve for P and \(\theta\), we resolve the forces horizontally and vertically, as the system is in equilibrium.

Resolving horizontally:

\(P \cos \theta = 32 \cos 20^\circ - 17 \sin 55^\circ\)

\(P \cos \theta = 16.1446\)

Resolving vertically:

\(P \sin \theta = 40 + 17 \cos 55^\circ - 32 \sin 20^\circ\)

\(P \sin \theta = 38.8062\)

Using Pythagoras' theorem to find P:

\(P = \sqrt{(17 \cos 55^\circ - 32 \sin 20^\circ + 40)^2 + (32 \cos 20^\circ - 17 \cos 35^\circ)^2}\)

\(P = 42.0\)

Using trigonometry to find \(\theta\):

\(\theta = \arctan \left( \frac{17 \cos 55^\circ - 32 \sin 20^\circ + 40}{32 \cos 20^\circ - 17 \cos 35^\circ} \right)\)

\(\theta = 67.4\)