Answer
550 feet
Work Step by Step
$y =$ height of building, $x = $distance from building after moving 400 feet closer
$tan (45) = y/x$
$1 = y/x$
$x=y$
$tan (30) = y/(400+y)$
$.5773 = y/(400+y)$
$.5773*(400+y) = y/(400+y)*(400+y)$
$230.92+.5773y = y$
$230.92+.5773y-.5773y = y-.5773y$
$230.92 = .4227y$
$230.92/.4227 = .4227y/.4227$
$546.3 = y$
