In the movies and television the ratio of the width to the screen to the height is called the aspect ration. television screens usually have an aspect ratio of 4: 3, wild movie screens usually have an aspect ratio of 1.85: 1. however if a movie is made for television in "letterbox" format, it retains the 1.85 : 1 aspect ratio and fills the top and bottom part of the screen with black bars. what would be the height of a movie in letterbox format on a television screen that measures 25 inches long its diagonal

Firstly, we have to find the height and width of the TV. We only have its diagonal...so you know the diagonal is given by summing the square of the width plus the square of the height. We can make the lenght 4x and width 3x.

(4x)^2+(3x)^2 = 25^2

16x^2 + 9x^2 = 625

25x^2 = 625

Divide both sides for 25

x^2 = 25

To find x square root both sides.

x = 5

Multiply the x for the unknown width and height

4*5 = 20 (height)
3*5 = 15 (width)

Set the proportion

Movie height : movie width = TV height : tv width

1 : 1.85 = x : 20

Multiply 1 and 20 and divide for 1.85

x = (20*1)/1.85 = 20/1.85 = 10,81 inches