We determine the true and the projected obliquity of HAT-P-36 and WASP-11/HAT-P-10 systems, respectively, which are both composed of a relatively cool star and a hot-Jupiter planet. Thanks to the high-resolution spectrograph HARPS-N, we observed the Rossiter-McLaughlin effect for both the systems by acquiring precise radial-velocity measurements during planetary transit events. We also present photometric observations comprising six light curves covering five transit events, obtained using three medium-class telescopes and the telescope-defocussing technique. One transit of WASP-11/HAT-P-10 was followed simultaneously from two observatories. The three transit light curves of HAT-P-36b show anomalies that are attributable to starspot complexes on the surface of the parent star, in agreement with the analysis of its spectra that indicate a moderate activity. By analysing the complete HATNet data set of HAT-P-36, we estimated the stellar rotation period by detecting a periodic photometric modulation in the light curve caused by star spots, obtaining Prot=15.3 days, which implies that the inclination of the stellar rotational axis with respect to the line of sight is 65 degree. We used the new spectroscopic and photometric data to revise the main physical parameters and measure the sky-projected misalignment angle of the two systems. We found lambda=-14 degree for HAT-P-36 and lambda=7 degree for WASP-11/HAT-P-10, indicating in both cases a good spin-orbit alignment. In the case of HAT-P-36, we also measured its real obliquity, which turned out to be 25 degrees.
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