To determine the height of each screen, we will use the Pythagorean Theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \(c\) is the diagonal of the screen, \(a\) is the width, and \(b\) is the height. Rearranging the formula to find the height \(b\) gives:
\[ b = \sqrt{c^2 - a^2} \]
Now, let's calculate the heights for each of the screens A, B, C, and D.
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
\[ b = \sqrt{40^2 - 35^2} = \sqrt{1600 - 1225} = \sqrt{375} \approx 19.36 \text{ inches} \]
Summary of Heights
- Screen A: Height ≈ 7.48 inches
- Screen B: Height ≈ 11.09 inches
- Screen C: Height ≈ 15.49 inches
- Screen D: Height ≈ 19.36 inches
Now, Yoselin's shelf has a height limit of 17 inches. The largest screen that fits on the shelf will have the largest height that is still less than or equal to 17 inches.
Comparing the heights, we find that:
- Screen A: 7.48 inches
- Screen B: 11.09 inches
- Screen C: 15.49 inches
- Screen D: 19.36 inches (does not fit)
Thus, Screen C with a height of approximately 15.49 inches is the largest screen that will fit on Yoselin's shelf.
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