The investigation of a Yb³⁺ trigonal centre in KMgF₃ was carried out by means of ENDOR. Expressions for the frequencies for ENDOR transitions in trigonally distorted complexes for arbitrary magnetic field orientation with respect to the crystallographic axes were obtained. A structural model of the centre was determined. The parameters of interaction of Yb³⁺ with F ions of the nearest environment were also determined. A method to determine the absolute signs of the crystal field parameters B₄³ and B₆³ was suggested. The microscopic calculation of crystal lattice deformation in KMgF₃ near a paramagnetic impurity was carried out. The microscopic analysis of transferred hyperfine interaction parameters for an ion in a non-S state and having a local non-cubic symmetry, taking into account the effects of the spin polarisation of the outer filled 5s and 5p shells of the rare-earth ion, has been carried out for the first time.