We report on determining the optical constants of Ta in the sub-extreme ultraviolet (EUV) spectral range 5.0-24.0 nm from the angle-dependent reflectance (ADR) measured using monochromatized synchrotron radiation. Two sputtered samples with differing thicknesses were investigated. Complementarily x-ray reflectance was measured at shorter wavelengths and evaluated by Fourier transform to facilitate an unambiguous selection of a model for the data evaluation based on an inverse solution of the Fresnel's equations for a layered system. Bayesian inferences coupled with a Nested Sampling (NS) algorithm were utilized to derive the optical constants with their corresponding uncertainties. This report further emphasizes the applicability of an acclaimed NS algorithm on a high-dimensional inverse problem. We explore the possibility of addressing the correlations between the optical constants of thin films and their structural parameters based on other established studies.