Final answer:
To correct a sideslip caused by the loss of an engine, pilots apply rudder input opposite to the yaw and may bank into the working engine to achieve coordinated flight. An example of piloting skill in engine failure is the successful landing of the Gimli Glider.
Step-by-step explanation:
An aircraft may experience a sideslip upon the loss of an engine because of the imbalance in thrust between the remaining engine(s) and the inoperative one. This imbalance creates asymmetrical thrust, also known as 'thrust asymmetry', which causes the aircraft to yaw towards the dead engine. To correct a sideslip, pilots must apply rudder input in the direction opposite to the yaw to maintain coordinated flight, and often they will have to bank slightly into the operating engine to counter the asymmetrical lift.
A well-known incident involving an engine failure is the case of the Gimli Glider, where a Boeing 767 ran out of fuel and lost all power to its engines. Experienced pilots managed to land the aircraft safely without power, showcasing the importance of piloting skills in unusual situations.