From a point P on level ground the angle of elevation of the top of a tower is 30∘. After walking 40 m directly toward the tower to a point Q, the angle of elevation becomes 45∘.
a. (i) Draw a clearly labelled diagram to represent the situation.
b. (ii) Taking the height of the tower as h metres, write two equations that arise from the given information.
c. (iii) Solve the equations of part (ii) to find the height of the tower and the distance of point P from the foot of the tower.