  Multiplicity is a ubiquitous characteristic of massive stars. Multiple
systems offer us a unique observational constraint on the formation of
high-mass systems. Herschel 36 A is a massive triple system composed of a close
binary (Ab1-Ab2) and an outer component (Aa). We measured the orbital motion of
the outer component of Herschel 36 A using infrared interferometry with the
AMBER and PIONIER instruments of ESO's Very Large Telescope Interferometer. Our
immediate aims are to constrain the masses of all components of this system and
to determine if the outer orbit is co-planar with the inner one. Reported
spectroscopic data for all three components of this system and our
interferometric data allow us to derive full orbital solutions for the outer
orbit Aa-Ab and the inner orbit Ab1-Ab2. For the first time, we derive the
absolute masses of mAa = 22.3 +/- 1.7 M_sun, mAb1 = 20.5 +/- 1.5 M_sun and mAb2
= 12.5 +/- 0.9 M_sun. Despite not being able to resolve the close binary
components, we infer the inclination of their orbit by imposing the same
parallax as the outer orbit. Inclinations derived from the inner and outer
orbits imply a modest difference of about 22 deg. between the orbital planes.
We discuss this result and the formation of Herschel 36 A in the context of
Core Accretion and Competitive Accretion models, which make different
predictions regarding the statistic of the relative orbital inclinations.
