What is the approximate diagonal size for a screen that is 294.2 inches wide with an aspect ratio of 1.78:1?

To determine the approximate diagonal size of a screen that is 294.2 inches wide with an aspect ratio of 1.78:1, you start by understanding the relationship between the screen's width, height, and diagonal.

The aspect ratio of 1.78:1 means for every 1.78 units of width, there is 1 unit of height. To find the height of the screen, you can use the aspect ratio to calculate it.

First, the height can be found using the following formula:

Height = Width / Aspect Ratio

In this case:

Height = 294.2 inches / 1.78 ≈ 165.6 inches.

Now that you have both the width and height, you can apply the Pythagorean theorem to find the diagonal size of the screen:

Diagonal = √(Width² + Height²)

Substituting the values:

Diagonal = √(294.2² + 165.6²)

Diagonal = √(86777.64 + 27443.36)

Diagonal = √(114221) ≈ 338.2 inches.

When rounded to the nearest whole number, this gives approximately 337.5 inches. Thus, the correct