A clothing store fixes a rectangular plane mirror of length 0.90m on a wall with its top edge positioned 1.70m above the floor. Customers stand on the floor in front of the mirror to check their outfits.
(i) Derive an expression that links the customer’s height H (in metres), the height of the eyes above the floor E, the given mirror length, and the position of the mirror edges.
(ii) Using your expression, determine the greatest value of H for which a customer can still see the full image if the customer’s eyes are 1.60m above the floor.
(iii) Comment on whether a customer whose eyes are 1.40m above the floor but who is 1.75m tall will be able to see the entire image. Support your answer with suitable working.