The formula to use could be either max likely
range (NM) = 1.23√H1 + 1.23√H2 where H1 and H2 are the heights of
the transmitter and receiver in feet or 12√(Height
of the aircraft as a flight level). The second formula assumes a sea level
transmitter which makes the first formula is more appropriate in this case. So,
113NM = 1.23√169 + 1.23√H2
Therefore
113 ÷ 1.23 = (√169 + √H2)
(113 ÷ 1.23) - √169 =
√H2
And
H2 = [(113 ÷
1.23) - √169]2 = 6220ft or approximately FL60.
Most pilots, being fundamentally lazy, would
avoid this mathematical exercise by entering each of the four multi-choice
answers into the formula until they found an answer that gave a range of 113NM.
Either method is acceptable.