Respuesta :
Answer:
47
Step-by-step 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.
The length of the diagonal of Stacy's ceiling is 46,7.
What is the Pythagoras theorem?
Pythagoras Theorem (also called Pythagorean Theorem) is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle.
The ceiling of Stacy's living room is a square that is 33 ft long on each side. Stacy knows the diagonal of the ceiling from corner to corner must be longer than 33 ft, but she doesn't know how long it is.
By using Pythagoras theorem;
[tex]\rm Hypotenuse ^2=33^2+33^2\\\\ Hypotenuse ^2=1089+1089\\\\ Hypotenuse ^2=2178\\\\ Hypotenuse =46.9\\\\[/tex]
By using trigonometry;
[tex]\rm Cos45=\dfrac{33}{d}\\\\d =\dfrac{33}{cos45}\\\\d=46.7[/tex]
Hence, the length of the diagonal of Stacy's ceiling is 46,7.
learn more about the Pythagoras theorem here;
https://brainly.com/question/343682
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