Question

50 points please help

The ceiling of Stacy's living room is a square that is 22 ft long on each side. Stacy knows the diagonal of the ceiling from corner to corner must be longer than 22 ft, but she doesn't know how long it is.

Solve for the length of the diagonal of Stacy's ceiling in two ways:

(a) Using the Pythagorean Theorem.

(b) Using trigonometry.

Round each answer to the nearest whole number and make sure to show all your work. (Hint: the answers should be the same!)

Answer 1

#a

• H²=P²+B²

P and B are sides of square

• H²=22²+22²
• H²=484+484
• H²=968
• H≈22√2ft
• H≈31ft

#b

Apply cosines

• cos45=22/H
• 1/√2=22/H
• H=22√2ft=31ft