A semicircular arch AB of length 2L and a vertical tower PQ are situated in the same vertical plane. The feet A and B of the arch and the base Q of the tower are at the same horizontal level with B between A and Q. A man at A finds the tower hidden from his view due to the arch. He stands crawling up the arch and just sees the top most point P of the tower after covering a distance L/2 along the arch. He crawls further to the top most point of the arch and notes the angle of elevation of p at be θ.
Compute the height of the tower in terms of L and θ.
