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
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.
To calculate the height of each screen using the Pythagorean Theorem, we can use the formula:
height^2 = diagonal^2 - width^2
For Screen A:
height^2 = (15^2) - (13^2)
height^2 = 225 - 169
height^2 = 56
height = √56
height ≈ 7.48 inches
For Screen B:
height^2 = (22^2) - (19^2)
height^2 = 484 - 361
height^2 = 123
height = √123
height ≈ 11.09 inches
For Screen C:
height^2 = (32^2) - (28^2)
height^2 = 1024 - 784
height^2 = 240
height = √240
height ≈ 15.49 inches
For Screen D:
height^2 = (40^2) - (35^2)
height^2 = 1600 - 1225
height^2 = 375
height = √375
height ≈ 19.36 inches
The calculated height of each screen is:
Screen A: approximately 7.48 inches
Screen B: approximately 11.09 inches
Screen C: approximately 15.49 inches
Screen D: approximately 19.36 inches