To find the height of each screen using the Pythagorean Theorem, we can use the formula:
\[ a^2 + b^2 = c^2 \]
Where:
- \(c\) is the diagonal of the screen,
- \(a\) is the width of the screen,
- \(b\) is the height of the screen.
Given the width and diagonal of each screen, we can rearrange the formula to solve for the height \(b\):
\[ b = \sqrt{c^2 - a^2} \]
Now we will use this formula to calculate the height for each screen.
Calculations:
-
Screen A:
- Diagonal \(c = 15\) inches,
- Width \(a = 13\) inches. \[ b = \sqrt{15^2 - 13^2} = \sqrt{225 - 169} = \sqrt{56} \approx 7.48 \text{ inches} \]
-
Screen B:
- Diagonal \(c = 22\) inches,
- Width \(a = 19\) inches. \[ b = \sqrt{22^2 - 19^2} = \sqrt{484 - 361} = \sqrt{123} \approx 11.09 \text{ inches} \]
-
Screen C:
- Diagonal \(c = 32\) inches,
- Width \(a = 28\) inches. \[ b = \sqrt{32^2 - 28^2} = \sqrt{1024 - 784} = \sqrt{240} \approx 15.49 \text{ inches} \]
-
Screen D:
- Diagonal \(c = 40\) inches,
- Width \(a = 35\) inches. \[ b = \sqrt{40^2 - 35^2} = \sqrt{1600 - 1225} = \sqrt{375} \approx 19.36 \text{ inches} \]
Completed Table:
| Screen | Diagonal | Width | Height (approx) | |--------|----------|-------|------------------| | A | 15” | 13” | 7.48” | | B | 22” | 19” | 11.09” | | C | 32” | 28” | 15.49” | | D | 40” | 35” | 19.36” |
Finding the Largest Screen that Will Fit:
Yoselin's shelf dimensions are 17 inches tall and 50 inches wide. We need to find the largest screen that fits both the width and height constraints.
- Screen A (7.48” height): Fits, as 7.48” < 17” and 13” < 50”.
- Screen B (11.09” height): Fits, as 11.09” < 17” and 19” < 50”.
- Screen C (15.49” height): Fits, as 15.49” < 17” and 28” < 50”.
- Screen D (19.36” height): Does not fit, as 19.36” > 17”.
Conclusion:
The largest screen that will fit on Yoselin's shelf is Screen C with a diagonal of 32 inches.
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