We probe the spin dynamics in a thin magnetic film at ferromagnetic resonance by nuclear resonant scattering of synchrotron radiation at the 14.4 keV resonance of ^{57}Fe. The precession of the magnetization leads to an apparent reduction of the magnetic hyperfine field acting at the ^{57}Fe nuclei. The spin dynamics is described in a stochastic relaxation model adapted to the ferromagnetic resonance theory by Smit and Beljers to model the decay of the excited nuclear state. From the fits of the measured data, the shape of the precession cone of the spins is determined. Our results open a new perspective to determine magnetization dynamics in layered structures with very high depth resolution by employing ultrathin isotopic probe layers.