Trigonometry · Superchallenge problem

Points $A$, $B$, $C$ lie in that order on a straight, level road, with $AB = BC = 100$ m. A vertical tower stands on the level ground beside the road (not on it). The angles of elevation of the top of the tower, seen from $A$, $B$ and $C$, are $30^\circ$, $45^\circ$ and $60^\circ$. Find the height of the tower in metres.