Question

In movies and television, the ratio of the width of the screen to the height is called the aspect ratio. Television screens usually have an aspect ratio of 4 : 3, while 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 in the top and bottom parts 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 along its diagonal? (Hint: First find the width and height of the television screen

Answer 1

Screen's diagonal 25 inches, we need to find its height and width


`(width)/(height)=(4)/(3)`


`width = 4* (height )/(3)`

We know tv is a rectangle in shape
so


`width^2+height^2= diagonal^2 \\{((4)/(3) * height)}^2+ height ^2=625 \\ \\(25)/(9) height^2=625 \\height^2= {225} \\height= 15 \\width=(4)/(3) * 15=20`

width= 20 inches
height= 15 inches
So movie with 1.85:1 aspect ratio will occupy width of 20 inches, so its height


`(width)/(height) =(1.85)/(1) \\ \\height= (width)/(1.85) =(20)/(1.85) =10.81\text{ inches} \\`

So movie will occupy a height 0f 10.81 inches on tv