Final answer:
The patient's left arm should be positioned in external rotation for a transthoracic lateral projection to assess the proximal humerus after a possible fracture.
Step-by-step explanation:
The correct position of the patient's left arm for a transthoracic lateral projection to assess the proximal humerus, given the patient's condition with a possible left humeral fracture, is option 3) Left arm in an external rotation. In this position, the anterior surface of the arm moves away from the midline of the body. This positioning is crucial to obtain an accurate view of the humerus for diagnostic purposes while also taking into consideration the patient's comfort and the need to avoid further injury. Fractures of the humerus can be due to falls, blows, or direct impact, resulting in different types of fractures such as impacted, transverse, or spiral fractures of the humeral shaft, or distal humerus fractures including supracondylar and intercondylar fractures.