Example: "The desperately engaged ships continued the fight"
adjective: having ones attention or mind or energy engaged
Example: "Deeply engaged in conversation"
adjective: built against or attached to a wall
Example: "Engaged columns"
adjective: having services contracted for
Example: "The carpenter engaged (or employed) for the job is sick"
adjective: (used of toothed parts or gears) interlocked and interacting
Example: "The gears are engaged"
adjective: (of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line)
Example: "Receptionists' telephones are always engaged"