Question

The ceiling of Katie’s living room is a square that is 10 ft long on each side. Katie knows the diagonal of the ceiling from corner to corner must be longer than 10 ft, but she doesn’t know how long it is.
Solve for the length of the diagonal of Katie’s ceiling in two ways. Be sure to show your work for each method. Round to the nearest whole number. Your answers should be the same.

a. Using the Pythagorean Theorem











b. Using Trigonometry Ratios (Hint: what angle is formed when you cut the square diagonally?)

Answer 1

Answer:

Answer: 14 feet. a. The Pythagorean theorem is a^2 + b^2 = c^2, where a and b are the sides of a right angle. By plugging in the sides of the wall, and solving for c, you can find the answer. 10^2 + 10^2 = c^2

| 100 + 100 = c^2 | 200 = c^2 | c = sqrt 200 | c = 14. The other way to solve this would be using the trig functions. You know that the angle between the hypotenuse and the wall side is 45 degrees, so you can use Sine to determine the hypotenuse. Sine is equal to opposite over hypotenuse. Sin (45) = 10/h | Sin (45) * h = 10 | h = 10/Sin (45) | h = 14. Both of the methods result in 14.

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Step-by-step explanation: