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 below. A: diagonal 15 width 13, B: diagonal 22 width 19, C: diagonal 32 width 28, D: diagonal 40 width 35. Use the Pythagorean theorem to calculate the height of each screen, and complete the table

Question

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 below. A: diagonal 15 width 13, B: diagonal 22 width 19, C: diagonal 32 width 28, D: diagonal 40 width 35. Use the Pythagorean theorem to calculate the height of each screen, and complete the table

Answer 1

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:

Screen A:
height = √(15^2 - 13^2)
height = √(225 - 169)
height = √56
height ≈ 7.48 inches

Screen B:
height = √(22^2 - 19^2)
height = √(484 - 361)
height = √123
height ≈ 11.09 inches

Screen C:
height = √(32^2 - 28^2)
height = √(1024 - 784)
height = √240
height ≈ 15.49 inches

Screen D:
height = √(40^2 - 35^2)
height = √(1600 - 1225)
height = √375
height ≈ 19.36 inches

Let's complete the table:

| Screen | Diagonal | Width | Height |
|--------|----------|-------|--------|
| A | 15 | 13 | 7.48 |
| B | 22 | 19 | 11.09 |
| C | 32 | 28 | 15.49 |
| D | 40 | 35 | 19.36 |

Now you have the height of each screen. You can use this information to determine which screen will fit on the 17-inch tall shelf.

Answer 2

To calculate the height of each screen using the Pythagorean theorem, we can use the formula:

Height^2 = Diagonal^2 - Width^2

Let's calculate the height for each screen:

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

Now, let's complete the table:

| Screen | Diagonal | Width | Height |
|--------|----------|-------|--------|
| A | 15 | 13 | 7.48 |
| B | 22 | 19 | 11.09 |
| C | 32 | 28 | 15.49 |
| D | 40 | 35 | 19.36 |