Screen Size
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
Diagonal
Width
Height
A
15"
13"
B
22"
19
C
32"
28"
D
40°
35"
1. Use the Pythagorean Theorem to calculate the height of each screen, and complete the table.
Screen Diagonal Width Height
A 15" 13" 7.82"
B 22" 19" 13.95"
C 32" 28" 18.33"
D 40" 35" 23.87"
Next question is
Which screen is the largest that will fit on Yoselin’s shelf?
The largest screen that will fit on Yoselin's shelf is Screen D with a diagonal of 40 inches, a width of 35 inches, and a height of 23.87 inches.
To use the Pythagorean Theorem to calculate the height of each screen, we can use the formula:
h = √(d^2 - w^2)
where h is the height, d is the diagonal, and w is the width.
Let's calculate the height for each screen:
Screen A:
h(A) = √(15^2 - 13^2)
= √(225 - 169)
= √56
≈ 7.48 inches
Screen B:
h(B) = √(22^2 - 19^2)
= √(484 - 361)
= √123
≈ 11.09 inches
Screen C:
h(C) = √(32^2 - 28^2)
= √(1024 - 784)
= √240
≈ 15.49 inches
Screen D:
h(D) = √(40^2 - 35^2)
= √(1600 - 1225)
= √375
≈ 19.36 inches
Now we have the heights for each screen:
Screen A: 7.48 inches
Screen B: 11.09 inches
Screen C: 15.49 inches
Screen D: 19.36 inches