We have studied structures of the chiral amino acid alanine adsorbed on Cu(110) via low-energy electron diffraction (LEED) as well as scattering of fast light atoms and molecules. The adsorption process was controlled in situ by the intensity of specularly reflected 2-keV He atoms. For projectile energies less than 1 keV, we applied the method of fast atom diffraction for studies on the structure of adsorbed alanine molecules on an atomically flat Cu(110) surface with focus on a p(3 x 2) adsorbate phase. The results are consistent with LEED and explain distortions in LEED patterns via an elongated surface unit cell with incommensurate c(3.16 x 2) symmetry of parts of the adsorbate. From triangulation using fast atoms via the azimuthal rotation of the target surface, the positions of protruding methyl groups are derived.