Final answer:
Referral to a cardiologist is the most appropriate next step for this patient, as she presents with signs indicative of a cardiac cause for her syncope.
Step-by-step explanation:
The most appropriate step in the management of this patient's syncope is referral to a cardiologist. The patient presents with a systolic murmur and a history suggestive of exertional angina relieved by nitroglycerin, which could indicate underlying cardiac conditions such as aortic stenosis or ischemic heart disease. The EKG findings of left ventricular hypertrophy support the likelihood of a cardiac pathology. Referral to a cardiologist is necessary for further evaluation with echocardiography and potentially other tests to define the exact cause of the syncope and direct appropriate management.