We used extreme ultraviolet (EUV) pulses to create transient gratings (TGs) with sub-100 nm spatial periodicity in a β-Ga_{2}O_{3} single crystal. The EUV TG launches acoustic modes parallel to the sample surface, whose dynamics were revealed via backward diffraction of a third, time-delayed, EUV pulse. In addition, the sharp penetration depth of EUV light launches acoustic modes along the surface normal with a broad wave vector spectrum. The dynamics of selected modes at a wave vector tangibly larger (≈1 nm^{-1}) than the TG one is detected in the time domain via the interference between the backward diffracted TG signal and the stimulated Brillouin backscattering of the EUV probe. While stimulated Brillouin backscattering of an optical probe was reported in previous EUV TG experiments, its extension to shorter wavelengths can be used as a contactless experimental tool for filling the gap between the wave vector range accessible by inelastic hard x-ray and thermal neutron scattering techniques, and the one accessible through Brillouin scattering of visible and UV light.