To find the height of a 29-inch TV given that its width is 20 inches, we can use the Pythagorean theorem. The theorem states that in 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).
We can represent this relationship with the equation:
\[ a^2 + b^2 = c^2 \]
where:
- \(c\) is the length of the diagonal (the size of the TV, 29 inches),
- \(a\) is the width (20 inches),
- \(b\) is the height (which we need to find).
Plugging in the values we have:
\[ 20^2 + h^2 = 29^2 \]
Calculating \(20^2\) and \(29^2\):
\[ 400 + h^2 = 841 \]
Now, we can isolate \(h^2\):
\[ h^2 = 841 - 400 \] \[ h^2 = 441 \]
Taking the square root of both sides to find \(h\):
\[ h = \sqrt{441} = 21 \]
Thus, the height of the TV is 21 inches. The Pythagorean triple (20, 21, 29) helps us to verify that these numbers form a valid right triangle since:
\[ 20^2 + 21^2 = 400 + 441 = 841 = 29^2 \]
So, the correct use of the Pythagorean theorem leads us to find that the height of the TV is indeed 21 inches.
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