We present Rossiter-McLaughlin observations of WASP-13b and WASP-32b and determine the sky-projected angle between the normal of the planetary orbit and the stellar rotation axis ($lambda$). WASP-13b and WASP-32b both have prograde orbits and are consistent with alignment with measured sky-projected angles of $lambda={8^{circ}}^{+13}_{-12}$ and $lambda={-2^{circ}}^{+17}_{-19}$, respectively. Both WASP-13 and WASP-32 have $T_{mathrm{eff}}<6250$K and therefore these systems support the general trend that aligned planetary systems are preferentially found orbiting cool host stars. A Lomb-Scargle periodogram analysis was carried out on archival SuperWASP data for both systems. A statistically significant stellar rotation period detection (above 99.9% confidence) was identified for the WASP-32 system with $P_{mathrm{rot}}=11.6 pm 1.0 $ days. This rotation period is in agreement with the predicted stellar rotation period calculated from the stellar radius, $R_{star}$, and $v sin i$ if a stellar inclination of $i_{star}=90^{circ}$ is assumed. With the determined rotation period, the true 3D angle between the stellar rotation axis and the planetary orbit, $psi$, was found to be $psi=11^{circ} pm 14$. We conclude with a discussion on the alignment of systems around cool host stars with $T_{mathrm{eff}}<6150$K by calculating the tidal dissipation timescale. We find that systems with short tidal dissipation timescales are preferentially aligned and systems with long tidal dissipation timescales have a broad range of obliquities.
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