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Answer :
To find the height of the TV, apply the Pythagorean theorem to the triangle formed by the height, width, and diagonal of the TV. Calculate the height as the square root of the difference between the square of the diagonal and the square of the width, which results in approximately 42 inches.
The question asks to find the height of a television given the diagonal measurement and the width. This is a classic example of a right triangle problem, where the television screen represents the hypotenuse of the triangle. To solve for the height, we can use the Pythagorean theorem which is expressed as
a2 + b2 = c2,
where c is the hypotenuse (diagonal), a is one leg (width), and b is the other leg (height).
We have the diagonal (80 inches) and the width (68 inches), so we plug these into the Pythagorean theorem:
682 + b2 = 802.
First we square the known sides:
4624 + b2 = 6400.
Next, we subtract the square of the width from the square of the diagonal to find the square of the height:
b2 = 6400 - 4624,
which results in
b2 = 1776.
Finally, we take the square root of both sides to find the height:
b = √1776, resulting in the height approximately equal to 42 inches.
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