A theoretical model has been developed to describe the behavior of exciton polaritons in a wide quantum well for structures with the zinc blende symmetry in a transverse magnetic field (the Voigt geometry). The model takes into account the mixing of the 1s-1s and 1s-2p states of heavy excitons by the magnetic field and makes it possible to explain and quantitatively describe the activation of optically inactive states in the reflection spectra and the magnetic-field-induced increase in the translational mass of the exciton. The quantitative calculations of the spectra have been preformed using typical parameters for CdTe/ZnCdTe quantum-well structures.