Polarized light Fourier transform infrared internal reflection spectroscopy (FT-IR/IRS) experiments indicate that for both Langmuir-Blodgett (LB) and self-assembled (SA) monolayers of stearate molecules at a fluorite (CaF2) surface the surfactant molecules are in the trans state with uniaxial distribution of both the hydrocarbon chains and the transition dipole moments of the CH2 stretching vibration. On this basis the average molecular orientation angles for such monolayers were determined from linear dichroism theory. In the case of the LB stearate monolayer the average molecular orientation angle was found to be 9-16 degrees from the surface normal whereas in the case of the SA stearate monolayer the average molecular orientation angle was found to be about 21 degrees from the surface normal.