Final answer:
The head-tilt, chin-lift maneuver is the best method to open the patient's airway.
Step-by-step explanation:
The BEST method to use to open her airway would be the head-tilt, chin-lift maneuver. This maneuver involves tilting the patient's head back and lifting their chin to open up the airway. It is the recommended method for opening the airway in a patient who is unconscious or unable to maintain their own airway. Other methods, such as the neck-lift, head-tilt maneuver and modified chin-lift maneuver, may not provide the same level of effectiveness.
It is important to note that the jaw-thrust maneuver is used specifically when there is a suspicion of a neck or spinal injury, as it avoids movement of the neck. However, in the given scenario of an unconscious patient found at the bottom of a dark stairway, the head-tilt, chin-lift maneuver would be the appropriate choice without the need for considering a potential neck or spinal injury.