PHASES Differential Astrometry and the Mutual Inclination of the V819 Herculis Triple Star System

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 +- 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.