Final answer:
The piriformis muscle is the one that passes through the greater sciatic foramen, originating in the anterior sacrum and attaching to the greater trochanter of the femur.
Step-by-step explanation:
The muscle that passes through the greater sciatic foramen is the piriformis muscle. This muscle originates in the anterior part of the sacrum and exits the pelvis through the greater sciatic foramen to attach to the greater trochanter of the femur. The piriformis is essential because it is involved in the lateral rotation and stabilization of the hip joint. When discussing muscles that produce movement to cross your legs, the sartorius is the correct answer. Another large muscle group mentioned, the gluteal muscles, particularly the gluteus maximus, attaches the leg to the pelvic girdle and is responsible for the extension of the hip joint.