Previous answer is incorrect.
It is a 30 60 90 triangle as described, but the short side of the triangle opposite the 30° angle is the length of the shadow, or 39".
Naomi is the long side of the triangle opposite the 60° angle. Therefore her height as a function of the length of the shadow is:
\(height = shadow \sqrt 3\)
\(height = 39 \sqrt3 \approx 67.5\)
Rounding the above to the nearest inch makes Naomi 68 inches tall, or 5 ft. 8".