Answer :
The height of the television to the nearest tenth of an inch is 9.6 inches.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in mathematics that describes the relationship between the sides of a right triangle. It states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).
To calculate the height of the television, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the television represents the hypotenuse of the right triangle, and the width and height represent the other two sides. Therefore, we can write:
[tex](diagonal)^2 = (width)^2 + (height)^2[/tex]
We know that the diagonal measures 24 inches, and the width is 22 inches. Let's plug in these values and solve for the height:
[tex](24)^2 = (22)^2 + (height)^2[/tex]
[tex]576 = 484 + (height)^2[/tex]
92 = [tex](height)^2[/tex]
[tex]height = \sqrt(92)[/tex]
height ≈ 9.6 inches
Therefore, the height of the television to the nearest tenth of an inch is 9.6 inches.
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