A decorative gateway is shaped as a semicircular arch whose straight base PQ is 20m long. A light is to be mounted at a point R on the curved edge such that the distance from P to R is 13m.
(i) Prove that △PRQ is a right-angled triangle.
(ii) Calculate the length QR.
(iii) The height of the arch at R is the perpendicular distance from R to the base PQ. Determine this height correct to one decimal place.