If you are at FL350 and pass directly over a TACAN, what should your DME read?

The correct answer is based on the altitude you are flying at and the characteristics of the TACAN navigation system. At 35,000 feet (FL350), the Distance Measuring Equipment (DME) readout should reflect the straight-line distance to the TACAN station in nautical miles.

To determine the DME reading, you can use the formula derived from the Pythagorean theorem, accounting for both the horizontal distance and vertical altitude. Since 1,000 feet of altitude corresponds to approximately 0.2 nautical miles horizontally, being at 35,000 feet means you would have an altitude of 35 nautical miles straight up from the ground level. As you fly directly over the TACAN, to find the DME, you combine this vertical component with the horizontal distance, which in this case, at a typical range for TACAN operations, would yield a DME reading of approximately 6 nautical miles.

Thus, when passing directly over the TACAN at FL350, your DME should read around 6 nautical miles, which aligns with the specifics of navigation systems and how they work at high altitudes.