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