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The decision to give the patient 15 grams of a simple carbohydrate is appropriate for this scenario due to the patient's presentation of hypoglycemia, characterized by a blood glucose level of 58 mg/dL, along with sweating, coldness, and clamminess. These symptoms indicate that the patient is experiencing a potential hypoglycemic episode, which requires immediate intervention to quickly raise blood sugar levels.

Simple carbohydrates, such as glucose tablets, orange juice, or regular soda, are rapidly absorbed into the bloodstream and can quickly increase blood glucose levels. This is crucial in cases of hypoglycemia to prevent further complications, such as loss of consciousness or seizures, which can occur if the condition is not treated promptly.

Rechecking blood glucose after intervention is typically done, but it would not be the best initial response in this case, as immediate action is necessary to address the hypoglycemic symptoms. Providing a complex carbohydrate wouldn’t be effective either, as they take longer to break down into sugars and thus do not address the immediate need for a rapid increase in blood glucose. Lastly, there is a critical need for intervention because a blood glucose level of 58 mg/dL is not considered normal, particularly in the context of the patient’s presenting symptoms.