The Collaborative International Dictionary of English v.0.48:

Engaged \En*gaged"\, a.
   1. Occupied; employed; busy.
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   2. Pledged; promised; especially, having the affections
      pledged; promised in marriage; affianced; betrothed.
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   3. Greatly interested; of awakened zeal; earnest.
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   4. Involved; esp., involved in a hostile encounter; as, the
      engaged ships continued the fight.
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   Engaged column. (Arch.) Same as Attached column. See
      under Attach, v. t.
      [1913 Webster]