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A certain television is advertised as a 95-inch TV (the diagonal length). If the width of the TV is 77 inches, how tall is the TV? Round to the nearest tenth of an inch.

Question

A certain television is advertised as a 95-inch TV (the diagonal length). If the width of the TV is 77 inches, how tall is the TV? Round to the nearest tenth of an inch.

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Solution

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the diagonal of the TV is the hypotenuse, and the width and height of the TV are the other two sides.

Here are the steps to solve the problem:

  1. Square the length of the diagonal: 95^2 = 9025
  2. Square the width of the TV: 77^2 = 5929
  3. Subtract the square of the width from the square of the diagonal: 9025 - 5929 = 3096
  4. Take the square root of the result to find the height: sqrt(3096) = 55.7

So, the height of the TV is approximately 55.7 inches, rounded to the nearest tenth of an inch.

This problem has been solved

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