You can launch a trigger with the AK::SoundEngine::PostTrigger() function:
AK::SoundEngine::PostTrigger( AK::TRIGGERS::PUZZLE_SOLVED, GAME_OBJECT_ID_HUMAN );
The AK::SoundEngine::PostTrigger() method also accepts strings (Unicode or Ansi) instead of IDs, in which case you would specify the name of the trigger, as defined by the Wwise user:
AK::SoundEngine::PostTrigger( L"Puzzle_Solved", GAME_OBJECT_ID_HUMAN );
Refer to Integration Details - Triggers for more details.