ranklein, I presume you already know the fundamentals of Pythagoras' theorem.
Hypotenuse = slant range from transmitter = 47nm.
Vertical distance = 30000' - 1500' = 28500' / 6080 = 4.69nm.
Therefore the horizontal distance = √(47² - 4.69²) = 46.77nm.
EET = 46.77 / 383 = 0.1221 hours = 7min 20 sec.