We have performed a type of Autler-Townes spectroscopy to locate a number of rovibrational-hyperfine levels of the a (3)Sigma(u)(+) potential, the lowest triplet potential of the Na-2 dimer. The spectroscopy starts with the photoassociation of ultracold atoms in a magneto-optical trap. We have measured the binding energies of over 100 individual states spanning the vibrational levels v=8-15 of this potential (binding energies up to 27 cm(-1)). We obtain a typical accuracy of 15 MHz and a typical resolution of 20 MHz, improving on the 10 GHz accuracy and 30 GHz resolution previously available for the vibrational states v<12. Vibrational, rotational, and hyperfine structures are resolved. Additionally, we have been able to resolve the magnetic electron-electron spin-spin dipole splitting of a number of these hyperfine levels. The measured rotational and hyperfine structures show good agreement with theoretical calculations. An analysis of the remaining discrepancies indicates where possible refinements to the potentials can be made. We also observe evidence for the presence of second-order spin-orbit coupling. (C) 2003 American Institute of Physics.