From a point P on level ground the angle of elevation of the top T of a tower is 45∘. After moving 30m closer to the tower to point Q, the angle of elevation becomes 60∘.
a. (i) Draw a labelled diagram representing the situation.
b. (ii) Form two equations involving the height of the tower and the initial horizontal distance of point P from the foot of the tower.
c. (iii) Solve the equations to determine the height of the tower.