To calculate the height of each screen using the Pythagorean Theorem, we can use the formula:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the diagonal of the screen,
- \( a \) is the width of the screen,
- \( b \) is the height of the screen.
Rearranging the formula to find the height \( b \):
\[ b = \sqrt{c^2 - a^2} \]
Now, let's calculate the height for each screen:
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
\[ b = \sqrt{40^2 - 35^2} = \sqrt{1600 - 1225} = \sqrt{375} \approx 19.36 \text{ inches} \]
Now, let's complete the table with the calculated heights:
| Screen | Diagonal | Width | Height | |--------|----------|-------|-----------| | A | 15” | 13” | 7.48” | | B | 22” | 19” | 11.09” | | C | 32” | 28” | 15.49” | | D | 40” | 35” | 19.36” |
Yoselin can use this information to choose the largest screen that will fit on her shelf with dimensions 17 inches tall and 50 inches wide. Based on the calculated heights, screens A, B, C, and just barely screen D can fit; however, the largest size that fits height-wise is screen D with a height of approximately 19.36 inches, which is too large for the 17-inch height maximum. So she would need to choose Screen C, which has a height of approximately 15.49 inches.
3 answers