V819 Herculis is a well-studied triple star system consisting of a “ wide ” pair with 5.5 year period , one component of which is a 2.2-day period eclipsing single-line spectroscopic binary . Differential astrometry measurements from the Palomar High-precision Astrometric Search for Exoplanet Systems ( PHASES ) are presented and used to determine a relative inclination between the short- and long-period orbits of 23.6 \pm 4.9 degrees . This represents only the sixth unambiguous determination of the mutual inclination of orbits in a hierarchical triple system . This result is combined with those for the other five systems for analysis of the observed distribution of mutual inclinations in nearby triple systems . It is found that this distribution is different than that which one would expect from random orientations with statistical significance at the 94 % level ; implications for studying the spatial distribution of angular momentum in star forming regions is discussed .