A large screen at a theater measures 65 feet diagonally. The aspect ratio (width compared to height) of the screen is 21:9. What is the approximate width and height of the screen?
(21^2 + 9^2) = 22.847
But your screen has diagonal of 65.
So, just multiply 9 and 21 by 65/22.847
To find the width and height of the screen, we can use the Pythagorean theorem because we have the diagonal and the aspect ratio.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (width and height).
Let's assume the width is 21x and the height is 9x (since the aspect ratio is given as 21:9).
According to the Pythagorean theorem, we have:
(diagonal)^2 = (width)^2 + (height)^2
(65 feet)^2 = (21x)^2 + (9x)^2
Simplifying this equation:
4225 = 441x^2 + 81x^2
Combining like terms:
4225 = 522x^2
Dividing both sides by 522:
x^2 = 8.10038610...
Taking the square root of both sides, we get:
x ≈ 2.84608003...
Therefore, the approximate value for x is around 2.85.
Now we can calculate the width and height:
Width = 21x ≈ 21 * 2.85 ≈ 59.85 feet
Height = 9x ≈ 9 * 2.85 ≈ 25.65 feet
So, the approximate width of the screen is 59.85 feet and the approximate height is 25.65 feet.