Which of the following is an indication of life-threatening airway obstruction in a child?

Cyanosis is an indication of life-threatening airway obstruction in a child because it signifies that the body, particularly the tissues, is not receiving sufficient oxygen. This can occur when the airway is significantly compromised, leading to impaired respiration. When tissues lack oxygen, they take on a bluish color, observed in areas such as the lips, face, or extremities.

In contrast, coughing forcefully is often a sign that the child is attempting to clear their airway and may still have a patent airway. Gurgling noises might suggest fluid in the airway but do not exclusively indicate a complete obstruction. Frequent throat clearing, while it may indicate irritation or a minor obstruction, does not demonstrate the severity of a life-threatening situation in the same way that cyanosis does. Thus, the presence of cyanosis is a critical sign that immediate intervention is necessary to restore a clear airway and oxygenation.