$zeta$ Phoenicis is a bright binary system containing B6V and B8V stars. It has deep total and annular eclipses, a slightly eccentric orbit with a period of 1.669 d, apsidal motion and a third body on a wider orbit. The Transiting Exoplanet Survey Satellite light curve and published radial velocities of this system are analysed to determine masses of 3.91 +/- 0.06 Msun and 2.54 +/- 0.03 Msun and radii of 2.84 +/- 0.02 Rsun and 1.89 +/- 0.01 Rsun. The resulting distance to the system is in agreement with its trigonometric parallax. The physical properties of the stars, with the exception of the effective temperature of the secondary component, can be matched by the predictions of several sets of theoretical stellar evolutionary models for a solar chemical composition and an age of 70 to 90 Myr. A spectroscopic analysis of this system is encouraged for the determination of the photospheric chemical composition of the stars, plus improved measurements of their masses and effective temperatures.
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