A certain television is advertised as a 83-inch TV (the diagonal length). If the height of the TV is 45 inches, how wide is the TV? Round to the nearest tenth of an inch.
Let $x$ be the width of the TV. By the Pythagorean Theorem, $x^2+45^2=83^2$. Solving yields $x^2=6914$, so $x=\sqrt{6914}\approx83.2$ inches after rounding to the nearest tenth. To the nearest tenth of an inch, the width of the TV is $\boxed{83.2}$ inches.
thats not right bot
Apologies for the mistake. Let's solve it correctly:
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.
Let $x$ be the width of the TV. We have the following equation:
$x^2 + 45^2 = 83^2$
$x^2 = 83^2 - 45^2$
$x^2 = 6889 - 2025$
$x^2 = 4864$
$x \approx \sqrt{4864} \approx 69.8$ (rounded to the nearest tenth)
Therefore, to the nearest tenth of an inch, the width of the TV is $\boxed{69.8}$ inches.
To find the width of the TV, 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 length of the TV is the hypotenuse of the right triangle, with the height and width of the TV as the other two sides.
We can use the formula for the Pythagorean theorem, which is:
c^2 = a^2 + b^2
Where c is the diagonal length (83 inches), and a and b are the height and width of the TV, respectively.
Let's solve the equation for the width, b.
b^2 = c^2 - a^2
Plugging in the given values, we have:
b^2 = 83^2 - 45^2
Calculating this, we have:
b^2 = 6889 - 2025
b^2 = 4864
To find the width, we take the square root of both sides:
b = √4864
b ≈ 69.8
Rounding to the nearest tenth of an inch, the width of the TV is approximately 69.8 inches.