We present a multitechnique approach to experimentally determine the elastic anisotropy of polycrystalline hcp Fe at high pressure. Directional phonon measurements from inelastic X-ray scattering on a sample with lattice preferred orientation at 52 GPa in a diamond anvil cell were coupled with X-ray diffraction data to determine the elastic tensor. Comparison of the results from this new method with the elasticity determined by lattice strain analysis of radial X-ray diffraction measurements showed significant differences, highlighting the importance of strength anisotropy in hcp Fe. At 52 GPa, we found that a method which combines results from inelastic scattering and pressure-volume measurements gives a shape in the velocity anisotropy close to sigmoidal (with a faster c and slower a axis) a smaller magnitude in the anisotropy and compared to velocities based on the lattice strain method which gives a bell shape velocity distribution with the fast direction between the c and a axes. We used additional results from nuclear resonant inelastic X-ray scattering to constrain errors and provide additional validation of the accuracy of our results.