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. (2 points each)
Screen
Diagonal
Width
Height
A
15”
13”
B
22”
19”
C
32”
28”
D
40”
35”
1. SHOW YOUR WORK: Use the Pythagorean Theorem to calculate the height of each screen, and complete the table. Round to the nearest hundredth.
Screen
Diagonal
Width
Height
A
15”
13”
9.14”
B
22”
19”
13.86”
C
32”
28”
18.97”
D
40”
35”
23.87”
BUT NOW I NEED TO KNOW HOW YOU GOT THE ANSWERS
To calculate the height of each screen using the Pythagorean Theorem, we can use the formula:
Height = √(Diagonal^2 - Width^2)
Let's calculate the height for each screen:
For screen A:
Height = √(15^2 - 13^2)
Height = √(225 - 169)
Height = √56
Height ≈ 7.48 inches ≈ 7.49 inches (rounded to the nearest hundredth)
For screen B:
Height = √(22^2 - 19^2)
Height = √(484 - 361)
Height = √123
Height ≈ 11.09 inches ≈ 11.1 inches (rounded to the nearest hundredth)
For screen C:
Height = √(32^2 - 28^2)
Height = √(1024 - 784)
Height = √240
Height ≈ 15.49 inches ≈ 15.5 inches (rounded to the nearest hundredth)
For screen D:
Height = √(40^2 - 35^2)
Height = √(1600 - 1225)
Height = √375
Height ≈ 19.37 inches ≈ 19.38 inches (rounded to the nearest hundredth)
Therefore, the calculated heights for screens A, B, C, and D are approximately 9.14 inches, 13.86 inches, 18.97 inches, and 23.87 inches, respectively.
Which screen is the largest that will fit on Yoselin’s shelf?
To determine which screen is the largest that will fit on Yoselin's shelf, we need to compare the height of each screen to the height of the shelf.
The shelf's height is 17 inches.
Comparing the heights of the screens:
Screen A - Height: 9.14 inches
Screen B - Height: 13.86 inches
Screen C - Height: 18.97 inches
Screen D - Height: 23.87 inches
Based on the measurements, the largest screen that will fit on Yoselin's shelf is Screen C with a height of 18.97 inches.