Self-consistent solutions to the plasma density and flow profile are obtained to the steady-state, isothermal hydrodynamic equations including the ponderomotive force for obliquely incident light when the upstream flow velocity is supersonic. The coupled set of hydrodynamic equations and the wave equation is solved numerically using an iterative procedure that adjusts the initial guess until a self-consistent solution is found. The fraction of light absorbed resonantly and the sensitivity of this fraction to plasma parameters are obtained.