We present our analysis of HD 35502 based on high-and medium-resolution spectropolarimetric observations. Our results indicate that the magnetic B5IVsnp star is the primary component of a spectroscopic triple system and that it has an effective temperature of 18.4 ± 0.6 kK, a mass of 5.7 ± 0.6 M , and a polar radius of 3.0 +1.1 −0.5 R . The two secondary components are found to be essentially identical A-type stars for which we derive effective temperatures (8.9 ± 0.3 kK), masses (2.1 ± 0.2 M ), and radii (2.1±0.4 R ). We infer a hierarchical orbital configuration for the system in which the secondary components form a tight binary with an orbital period of 5.66866(6) d that orbits the primary component with a period of over 40 yrs. Least-Squares Deconvolution (LSD) profiles reveal Zeeman signatures in Stokes V indicative of a longitudinal magnetic field produced by the B star ranging from approximately −4 to 0 kG with a median uncertainty of 0.4 kG. These measurements, along with the line variability produced by strong emission in Hα, are used to derive a rotational period of 0.853807(3) d. We find that the measured v sin i = 75 ± 5 km s −1 of the B star then implies an inclination angle of the star's rotation axis to the line of sight of 24 +6 −10°. Assuming the Oblique Rotator Model, we derive the magnetic field strength of the B star's dipolar component (14 +9 −3 kG) and its obliquity (63 ± 13°). Furthermore, we demonstrate that the calculated Alfvén radius (41 +17 −6 R * ) and Kepler radius (2.1 +0.4 −0.7 R * ) place HD 35502's central B star well within the regime of centrifugal magnetosphere-hosting stars.