Points A and B are 56.0 m apart along an east-west line. At each of these points, a radio transmitter is emitting a 12.5-MHz signal horizontally. These transmitters are in phase with each other and emit their beams uniformly in a horizontal plane. A receiver is taken 0.500 km north of the line and initially placed at point C directly opposite the midpoint of AB. The receiver can be moved only along an east-west direction but, due to its limited sensitivity, it must always remain within a range so that the intensity of the signal it receives from the transmitter is no less than 1/4 of its maximum value. How far from point C (along an east-west line) can the receiver be moved and always be able to pick up the signal?
The Attempt at a Solution
(Sorry my bad English). The difference between the two paths should be 8 m. I've drawn a sketch for the situation and using a calculator I found x to be something greater than 44m. Then the distance is (28 + 44)m ≅ 72m, but it doesn't agree with the book answer: 71.4m. I know that it's a small difference, but it doesn't seems to me that the author would put this answer for no reason.