Computer screens and television screens are usually measured by the diagonal of
the screen. For example, a screen of size 60 inches would have a diagonal of 60
inches, a width of 52 inches, and a height of 30 inches.
Yoselin would like to install a new screen on a shelf that is 17 inches tall and 50
inches wide. She would like the screen to be the largest size that will fit on the
shelf. She knows the diagonal and width of the 4 screens listed below.
Screen: A, B, C, D
Diagonal : A: 15", B: 22", C: 32", D: 40"
Width: A: 13", B: 19", C: 28", D: 35".
Use the Pythagorean Theorem to calculate the height of each screen, and complete the table.
Screen A:
Diagonal = 15", Width = 13"
Using the Pythagorean Theorem, we can calculate the height.
Height^2 = Diagonal^2 - Width^2
Height^2 = 15^2 - 13^2
Height^2 = 225 - 169
Height^2 = 56
Height ≈ √56
Height ≈ 7.48 inches
Screen B:
Diagonal = 22", Width = 19"
Height^2 = 22^2 - 19^2
Height^2 = 484 - 361
Height^2 = 123
Height ≈ √123
Height ≈ 11.09 inches
Screen C:
Diagonal = 32", Width = 28"
Height^2 = 32^2 - 28^2
Height^2 = 1024 - 784
Height^2 = 240
Height ≈ √240
Height ≈ 15.49 inches
Screen D:
Diagonal = 40", Width = 35"
Height^2 = 40^2 - 35^2
Height^2 = 1600 - 1225
Height^2 = 375
Height ≈ √375
Height ≈ 19.36 inches
Completing the table:
Screen A: Diagonal = 15", Width = 13", Height ≈ 7.48 inches
Screen B: Diagonal = 22", Width = 19", Height ≈ 11.09 inches
Screen C: Diagonal = 32", Width = 28", Height ≈ 15.49 inches
Screen D: Diagonal = 40", Width = 35", Height ≈ 19.36 inches
Is that the right height bot? its for a test
Apologies for the incorrect information. Let me recalculate the heights of each screen using the Pythagorean Theorem.
Screen A:
Diagonal = 15", Width = 13"
Height^2 = Diagonal^2 - Width^2
Height^2 = 15^2 - 13^2
Height^2 = 225 - 169
Height^2 = 56
Height ≈ √56
Height ≈ 7.48 inches
Screen B:
Diagonal = 22", Width = 19"
Height^2 = Diagonal^2 - Width^2
Height^2 = 22^2 - 19^2
Height^2 = 484 - 361
Height^2 = 123
Height ≈ √123
Height ≈ 11.09 inches
Screen C:
Diagonal = 32", Width = 28"
Height^2 = Diagonal^2 - Width^2
Height^2 = 32^2 - 28^2
Height^2 = 1024 - 784
Height^2 = 240
Height ≈ √240
Height ≈ 15.49 inches
Screen D:
Diagonal = 40", Width = 35"
Height^2 = Diagonal^2 - Width^2
Height^2 = 40^2 - 35^2
Height^2 = 1600 - 1225
Height^2 = 375
Height ≈ √375
Height ≈ 19.36 inches
Please note that the heights I provided earlier were correct.
2. Which screen is the largest that will fit on Yoselin’s shelf?
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To calculate the height of each screen, we can use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the width and height of the screen form the two sides of the right-angled triangle, and the diagonal represents the hypotenuse.
Let's calculate the height for each screen:
For Screen A:
We know the width is 13 inches and the diagonal is 15 inches.
Using the Pythagorean Theorem, we can calculate the height as:
height^2 = diagonal^2 - width^2
height^2 = 15^2 - 13^2
height^2 = 225 - 169
height^2 = 56
height ≈ √56
height ≈ 7.48 inches (rounded to two decimal places)
For Screen B:
We know the width is 19 inches and the diagonal is 22 inches.
Using the Pythagorean Theorem, we can calculate the height as:
height^2 = diagonal^2 - width^2
height^2 = 22^2 - 19^2
height^2 = 484 - 361
height^2 = 123
height ≈ √123
height ≈ 11.09 inches (rounded to two decimal places)
For Screen C:
We know the width is 28 inches and the diagonal is 32 inches.
Using the Pythagorean Theorem, we can calculate the height as:
height^2 = diagonal^2 - width^2
height^2 = 32^2 - 28^2
height^2 = 1024 - 784
height^2 = 240
height ≈ √240
height ≈ 15.49 inches (rounded to two decimal places)
For Screen D:
We know the width is 35 inches and the diagonal is 40 inches.
Using the Pythagorean Theorem, we can calculate the height as:
height^2 = diagonal^2 - width^2
height^2 = 40^2 - 35^2
height^2 = 1600 - 1225
height^2 = 375
height ≈ √375
height ≈ 19.36 inches (rounded to two decimal places)
Complete table:
Screen: A, B, C, D
Diagonal: A: 15", B: 22", C: 32", D: 40"
Width: A: 13", B: 19", C: 28", D: 35".
Height: A: 7.48", B: 11.09", C: 15.49", D: 19.36"