We determine the exact physical parameters of the four Hyades cluster K giants, using their parallaxes and atmospheric modelling of our red-channel TIGRE high-resolution spectra. Performing a comparison with well-tested evolutionary tracks, we derive exact masses and evolutionary stages. At an age of 588 (+/- 60) Myr and with a metallicity of Z = 0.03 (consistent with the spectroscopic abundances), we find HD27371 and HD28307, the two less bright K giants, at the onset of central helium burning, entering their blue loops with a mass of 2.62 M-circle dot, while the slightly brighter stars HD28305 and HD27697 are already exiting their blue loop. Their more advanced evolution suggests a higher mass of 2.75 M-circle dot. Notably, this pairing coincides with the different activity levels, which we find for these four stars from chromospheric activity monitoring with TIGRE and archival Mount Wilson data as well as from ROSAT coronal detections. The two less evolved K giants are the far more active pair, and we confidently confirm their rotation with periods of about 142 d. This work therefore provides some first, direct evidence of magnetic braking during the 130 Myr lasting phase of central helium-burning, similar to what has long been known to occur to cool main-sequence stars.