Mechanics: Finding the minimum force required?

This is to do with Mechanics 1B for A2 Maths.
A particle of W=39.2 is suspended in equilibrium from a vertical wall by a string. A force P is applied to pull it 50 cm away from the wall. As a result (due to some further calculations I did) the T in the string has an angle of 112.6 to the horizontal. What is the minimum P required?

How does one go about finding the angle needed for the force to be at its minimum? If I knew that I could solve the question.

What I did:
I thought P would have an angle that is opposite to the angle of the resultant of the two other forces, T and W. However I couldn't find the resultant because one of the forces in unknown and I don't know all the angles.