Joey's living room is a square that is 33 ft long on each side. He knows the diagonal of the ceiling from corner to corner must be longer than 33 ft. (a) He thinks that because a square cut in half forms a special right triangle with the diagonal as the hypotenuse, so he multiplies the side length by two to get 66 feet. What is Joey's mistake?
(b) What is the correct length of the diagonal of Joey's ceiling using the correct special right triangle shortcut? (give exact answer, no rounding)
(c) Use either the Pythagorean Theorem OR the correct trigonometry ratios to solve for the length of the diagonal (round to nearest tenth of a foot)
Make sure to show all your work.
