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Answer :
To solve the problem of finding the height of the TV screen, we can use the Pythagorean theorem. This theorem is applicable because the diagonal, length, and height of the TV screen form a right triangle. The formula is:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
Where:
- [tex]\( a \)[/tex] is one side of the triangle (the height we need to find),
- [tex]\( b \)[/tex] is the other side of the triangle (given as 38 inches, the length),
- [tex]\( c \)[/tex] is the hypotenuse of the triangle (the diagonal of the screen, given as 45 inches).
We need to rearrange this formula to solve for the height ([tex]\( a \)[/tex]):
[tex]\[ a^2 = c^2 - b^2 \][/tex]
Now, let's plug in the given values:
1. Calculate the square of the diagonal (hypotenuse):
[tex]\[ 45^2 = 2025 \][/tex]
2. Calculate the square of the length:
[tex]\[ 38^2 = 1444 \][/tex]
3. Subtract the square of the length from the square of the diagonal:
[tex]\[ a^2 = 2025 - 1444 = 581 \][/tex]
4. To find the height, take the square root of 581:
[tex]\[ a \approx \sqrt{581} \approx 24.1 \][/tex]
Therefore, the height of the TV screen is approximately 24 inches, which corresponds to option B.
[tex]\[ a^2 + b^2 = c^2 \][/tex]
Where:
- [tex]\( a \)[/tex] is one side of the triangle (the height we need to find),
- [tex]\( b \)[/tex] is the other side of the triangle (given as 38 inches, the length),
- [tex]\( c \)[/tex] is the hypotenuse of the triangle (the diagonal of the screen, given as 45 inches).
We need to rearrange this formula to solve for the height ([tex]\( a \)[/tex]):
[tex]\[ a^2 = c^2 - b^2 \][/tex]
Now, let's plug in the given values:
1. Calculate the square of the diagonal (hypotenuse):
[tex]\[ 45^2 = 2025 \][/tex]
2. Calculate the square of the length:
[tex]\[ 38^2 = 1444 \][/tex]
3. Subtract the square of the length from the square of the diagonal:
[tex]\[ a^2 = 2025 - 1444 = 581 \][/tex]
4. To find the height, take the square root of 581:
[tex]\[ a \approx \sqrt{581} \approx 24.1 \][/tex]
Therefore, the height of the TV screen is approximately 24 inches, which corresponds to option B.
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