The 3D orientation of a single gold nano-bipyramid (AuBPs) on a glass substrate is successfully measured by polarimetric analysis of its scattering. The AuBPs are very attractive due to the presence of hot spots at their end tips resulting from a strong longitudinal localized surface plasmon resonance. In addition, this resonance can be modeled as a radiating dipole. To study the 3D orientation, we designed a specific spectroscopic dark-field microscope with a precise control of the collection angles of the scattering in the Fourier plane. The 3D angles are resolved by analyzing the polarization of the AuBP scattering. Simulations are used to extract the inplane and out-of-plane angles with a very good accuracy of 3 %. In particular, the critical role of the numerical aperture collection was investigated experimentally by Fourier filtering of the scattering into the back focal plane of the objective. It reveals a physical insight into the contribution of the evanescence waves and provides a technical guideline for choosing the collection objective for polarimetric measurements.