To find the height of a screen given its diagonal and width, we use the Pythagorean theorem. The theorem states that for a right triangle, the square of the length of the hypotenuse (the diagonal, in this case) is equal to the sum of the squares of the other two sides (the width and height).
Mathematically, this can be expressed as:
\[ d^2 = w^2 + h^2 \]
Where:
- \(d\) is the diagonal,
- \(w\) is the width,
- \(h\) is the height.
Given the shelf height of 17 inches, we need to calculate the height for each screen size mentioned in your query. However, you have not provided the specific diagonal and width values for the 4 screens. Nonetheless, I will describe the process for completing the calculations.
Example Calculation Steps:
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For each screen, you'll need to know the dimensions:
- Diagonal (d)
- Width (w)
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Rearranging the equation to solve for height \(h\):
\[ h = \sqrt{d^2 - w^2} \]
- Plug in the values for \(d\) and \(w\) for each screen to find \(h\).
Example Entry:
Assume we have the following four screens (this is just an example; you'd use the actual values you have):
- Screen 1: 60 inches diagonal, 52 inches width
- Diagonal (d) = 60
- Width (w) = 52
\[ h = \sqrt{60^2 - 52^2} = \sqrt{3600 - 2704} = \sqrt{896} \approx 29.93 \text{ inches} \]
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Screen 2: (add your screen details)
- Diagonal (d) = X inches
- Width (w) = Y inches
- Compute height using the formula.
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Repeat for Screens 3 and 4.
Completed Table Example:
| Screen | Diagonal (inches) | Width (inches) | Height (inches) | |--------|--------------------|-----------------|------------------| | 1 | 60 | 52 | 29.93 | | 2 | X | Y | (calculated h) | | 3 | X | Y | (calculated h) | | 4 | X | Y | (calculated h) |
Make sure to replace \(X\) and \(Y\) with the actual measurements for screens 2 to 4, and compute the heights accordingly.
When you have the specific diagonal and width values for each screen, I’d be happy to help you further calculate the heights!
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