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The diagonal of Andre's rectangular TV screen is 39 inches. The width of his TV screen is 34 inches. Which measurement is closest to the height of Andre's TV screen? A. 8.5 inches B. 19.1 inches C. 36.5 inches D. 51.7 inches

The diagonal of Andre's rectangular TV screen is 3939 inches. The width of his TV T V screen is 3434 inches. Which measurement is closest to the height of Andre's TV screen?\newlineA. 88.55 inches\newlineB. 1919.11 inches\newlineC. 3636.55 inches\newlineD. 5151.77 inches

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Q. The diagonal of Andre's rectangular TV screen is 3939 inches. The width of his TV T V screen is 3434 inches. Which measurement is closest to the height of Andre's TV screen?\newlineA. 88.55 inches\newlineB. 1919.11 inches\newlineC. 3636.55 inches\newlineD. 5151.77 inches
  1. Pythagorean Theorem Application: To find the height of the TV screen, we can use the Pythagorean theorem, which states that in a right-angled 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. Here, the diagonal of the TV screen is the hypotenuse, and the width and height are the other two sides. Specifically, if the diagonal is dd, the width is ww, and the height is hh, then according to the Pythagorean theorem, d2=w2+h2d^2 = w^2 + h^2.
  2. Denote Height as 'h': Let's denote the height of the TV screen as 'h'. According to the Pythagorean theorem, we have:\newline(diagonal)2=(width)2+(height)2(\text{diagonal})^2 = (\text{width})^2 + (\text{height})^2\newlineSubstituting the given values, we get:\newline392=342+h239^2 = 34^2 + h^2
  3. Calculate Diagonal and Width Squares: Now, we calculate the squares of the diagonal and the width:\newline392=152139^2 = 1521\newline342=115634^2 = 1156
  4. Substitute Values into Equation: Next, we substitute these values into the equation: 1521=1156+h21521 = 1156 + h^2
  5. Solve for ' extit{h}^22': We then solve for ' extit{h}^22' by subtracting the square of the width from the square of the diagonal:\newlineh2=1521−1156h^2 = 1521 - 1156\newlineh2=365h^2 = 365
  6. Find Height 'h': Now, we take the square root of both sides to find the height 'h':\newlineh=365h = \sqrt{365}\newlineh≈19.1h \approx 19.1 inches

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