Sizing here is a gerund. Gerunds aren't verbs, but they are derived and related to verbs. Sizing here in particular is a "verbal" form of to size that is functioning as a noun.
To size X means the equivalent of either
-ing words in general mean "the action of" - e.g. walking = the action of walking, sizing = the action of sizing.
Since sizing along with gerunds in general are nouns, most of the normal rules with articles apply. One exception is if a gerund has an object, then you don't use an article, e.g. I got in trouble for him sizing the equipment incorrectly.
Sizing is a definite event that is likely known from previous sentences or conversation, so the is called for here, versus a or no article.