Because PC vertical BC PA vertical BC gets BC vertical plane PAC gets BC vertical AC.

So the dihedral angle P-BC-A is the angle PCA.

∠ ABC = 30, so AC= 1/2BA.

PB makes an angle of 45 with the plane ABC, so the angle PBC = 45°, because A is the projection of P on the plane ABC.

So PA=AB, so AC= 1/2PA, so tan angle PCA=2.

So the dihedral angle P-BC-A is arctangent 2.