Ultracold atomic gases is a versatile platform for exploring quantum collective phenomena in strongly-interacting many-body systems. One of the most powerful techniques to probe the many-body state of the system is RF spectroscopy - a measurement of the number of atoms outcoupled by the RF pulse versus its frequency. From the lineshape many important physical observables can be retrieved. One of them is the contact which measures the change of energy with respect to the inverse of the scattering length. The contact is also manifested as the spectral weight in the high energy part of the RF lineshape. So far, measurements of the contact were limited by the sensitivity needed to detect a relatively small number of atoms in the RF lineshape tail. We have developed a novel technique capable of resolving lineshape signals of only few atoms, extending the detectable region by a factor of 10 compared to previous techniques. We employ this technique to demonstrate the power law scaling of the RF lineshape tail over more than two decades, from which we extract the contact with unprecedented accuracy.