Since the system is in equilibrium, the sum of the forces in any direction is zero. We resolve the forces horizontally and vertically.

For horizontal components:

\(P \cos \theta = (36 - 24) \cos 36.9^{\circ}\)

\(P \cos \theta = 9.6\)

For vertical components:

\(P \sin \theta + 20 = (24 + 36) \sin 36.9^{\circ}\)

\(P \sin \theta + 20 = 36\)

\(P \sin \theta = 16\)

Using the equations:

\(P \cos \theta = 9.6\)

\(P \sin \theta = 16\)

We find \(P\) using:

\(P = \sqrt{16^2 + 9.6^2}\)

\(P = 18.7\)

To find \(\theta\):

\(\theta = \arctan \left( \frac{16}{9.6} \right)\)

\(\theta = 59.0^{\circ}\)