Forward intersection
γ = 180° − β₁ − β₂, AP = b·sin β₂ / sin γ, α_AP = α_AB ∓ β₁, then the direct problem.
Distance intersection
Angles by the law of cosines; two solutions, choose the side.
Resection
Two angles at P to three control points define two circles; their second intersection is P. Fails on the danger circle.