Final answer:
The vessel exposed during an anterior hip approach between the tensor fascia lata and sartorius muscle is a branch of the lateral circumflex artery, a branch of the deep femoral artery.
Step-by-step explanation:
The vessel that is exposed when crossing the interval between the tensor fascia lata and the sartorius muscle during an anterior approach to the hip is a branch of the lateral circumflex artery, which is itself a branch of the deep femoral artery. The lateral circumflex artery supplies blood to the deep muscles of the thigh and the ventral and lateral regions of the integument.
This is in the context of the femoral artery being a continuation of the external iliac artery after it passes through the body cavity, subsequently dividing into several smaller branches, including the lateral deep femoral artery, before becoming the popliteal artery as it passes posterior to the knee.