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This problem involves using the Pythagorean Theorem to find the width of the TV. The diagonal of the TV, the height, and the width form a right triangle, where:

- Diagonal = 83 inches (hypotenuse)
- Height = 45 inches (one leg)
- Width = unknown (other leg)

The Pythagorean Theorem states:
\[
\text{Diagonal}^2 = \text{Height}^2 + \text{Width}^2
\]
Plugging in the values:
\[
83^2 = 45^2 + \text{Width}^2
\]

We can now solve for the width. I'll compute this next.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can solve it by applying the following formula:

\[
\text{Width} = \sqrt{\text{Diagonal}^2 - \text{Height}^2}
\]

1. Square the diagonal and height:
\[
83^2 = 6889, \quad 45^2 = 2025
\]

2. Subtract the height squared from the diagonal squared:
\[
6889 - 2025 = 4864
\]

3. Take the square root of the result:
\[
\text{Width} = \sqrt{4864} \approx 69.7 \, \text{inches}
\]

So, the width of the TV is approximately 69.7 inches.

Let me know if you'd like more details, or have any other questions!

Here are 5 related questions for you:
1. How would you calculate the height if the width and diagonal are given instead?
2. Can you find the diagonal length if both width and height are known?
3. What are other real-life applications of the Pythagorean Theorem?
4. How does aspect ratio relate to TV dimensions?
5. How can you verify whether a given set of diagonal, height, and width forms a right triangle?

**Tip:** When dealing with triangles, the Pythagorean theorem only applies to right triangles! Always ensure your problem involves one.

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.

Learn how to calculate the width of an 83-inch TV, given a height of 45 inches, using the Pythagorean Theorem. This problem is suitable for students in Grades 7-10 and involves applying geometry and algebraic formulas to solve for the unknown side in a right triangle.

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