A 13 m long ladder rests against a smooth vertical wall and makes an angle of 60° with the horizontal ground. Without moving the foot of the ladder, it slides down the wall until it makes an angle of 45° with the ground.
a. (i) Calculate the height reached by the top of the ladder on the wall when the ladder is at 60°.
b. (ii) Calculate the height reached by the top of the ladder on the wall when the ladder is at 45°.
c. (iii) Hence determine the vertical distance through which the top of the ladder descends.