To solve for \(P\) and \(\theta\), we resolve the forces horizontally and vertically.

Given \(\tan \alpha = \frac{7}{24}\), we have \(\cos \alpha = \frac{24}{25}\) and \(\sin \alpha = \frac{7}{25}\).

Resolving horizontally:

\(P \cos \theta = 48 \cos \alpha - 14 \sin \alpha\)

\(P \cos \theta = 48 \left(\frac{24}{25}\right) - 14 \left(\frac{7}{25}\right) = 42.16\)

Resolving vertically:

\(P \sin \theta = 50 - 48 \sin \alpha - 14 \cos \alpha\)

\(P \sin \theta = 50 - 48 \left(\frac{7}{25}\right) - 14 \left(\frac{24}{25}\right) = 23.12\)

Using Pythagoras' theorem:

\(P = \sqrt{42.16^2 + 23.12^2} = 48.1\)

To find \(\theta\):

\(\tan \theta = \frac{23.12}{42.16}\)

\(\theta = 28.7^\circ\)