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 four screens listed below.
Screen
A
B
C
D
Diagonal
15
22
32
40
Width
13
19
28
35
Height
…
1. Use the Pythagorean Theorem to calculate the height of each screen.
2. Which screen is the largest that will fit on Yoselin’s shelf?
To calculate the height of each screen, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides (in this case, the width and height).
1. Using the Pythagorean Theorem, we can calculate the height for each screen:
Screen A:
Width^2 + Height^2 = Diagonal^2
13^2 + Height^2 = 15^2
169 + Height^2 = 225
Height^2 = 225 - 169
Height^2 = 56
Height ≈ √56
Height ≈ 7.48 inches
Screen B:
Width^2 + Height^2 = Diagonal^2
19^2 + Height^2 = 22^2
361 + Height^2 = 484
Height^2 = 484 - 361
Height^2 = 123
Height ≈ √123
Height ≈ 11.09 inches
Screen C:
Width^2 + Height^2 = Diagonal^2
28^2 + Height^2 = 32^2
784 + Height^2 = 1024
Height^2 = 1024 - 784
Height^2 = 240
Height ≈ √240
Height ≈ 15.49 inches
Screen D:
Width^2 + Height^2 = Diagonal^2
35^2 + Height^2 = 40^2
1225 + Height^2 = 1600
Height^2 = 1600 - 1225
Height^2 = 375
Height ≈ √375
Height ≈ 19.37 inches
2. The largest screen that will fit on Yoselin's shelf is Screen C, with a diagonal of 32 inches, a width of 28 inches, and a height of 15.49 inches.