The phenomenon of `moment canting`, where the atomic moments in a soft magnetic material do not completely align with an applied field of substantial magnitude, has been measured as a function of field in field annealed Fe₇₈Si₉B₁₃ metallic glass ribbons. Probability distributions for the Fe moment directions were deduced from unpolarized ⁵⁷Fe Mossbauer experiments. A method of analysis was devised to account for spectral saturation effects, and validated with reference to polycrystalline alpha -Fe. Fields of up to 0.5 T were applied at room temperature in the ribbon plane. Even in 0.5 T the in-plane moment canting did not fall to zero, with the standard deviation of the Gaussian spread in moment directions remaining at 12 degrees +or-1 degrees . Fields of up to 9 T were applied at 4.2 K, normal to the ribbon plane. Even in 9 T appreciable canting was observed, with a Gaussian standard deviation of 11 degrees +or-1 degrees with respect to the applied field direction. An a priori `combed hair` model was developed to describe the moment canting that would result from the presence of a few frustrated exchange interactions between some magnetic atoms. Long-distance moment canting was predicted, with a truncated inverse sine probability distribution. The data were found to be adequately described using this model.