Up, up and away
Suppose \(2015\) people of different heights are arranged in a straight line from shortest to tallest such that
(i) the tops of their heads are collinear, and
(ii) for any two successive people, the horizontal distance between them is equal to the height of the shorter of the two people.
If the shortest person is \(49\) inches tall and the tallest is \(81\) inches tall, then how tall is the person at the middle of the line, (in inches)?