Question

100 POINTS ANSWER ASAP

George'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 hypotense, so he multiples the side length by two to get 66 feet.
What is George's mistake?

(b) What is the correct length of the diagonal of George's ceiling using the correct special right triangle shortcut? (give exact answer, do not round)

(c) Use either the pythagorean theorem OR the correct trigonometry ratios to solve for the length of the diagonal (round to the nearest tenth of a foot)

Make sure to show all your work.

Answer 1

47. Hope that this helps!

Answer 2

47

Explanation:

a)

a^2 + b^2 = c^2

33^2+33^2=c^2

2178=c^2

c=(nearest is 47)

b)

If you cut the square in half diagonally, it forms two right triangles with angle measures 90-45-45. You can use sin (opposite over hypotenuse) to find the length of the hypotenuse. sin (45) would be 33/(hypotenuse length). From a trig chart, you can find that sin (45) is 1/sqrt(2), meaning that 33/x = 1/sqrt(2). This means that x=33sqrt(2), which is around 47.