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

$\frac{width}{height}=\frac{4}{3}$

$width = 4\times \frac{height }{3}$

We know tv is a rectangle in shape
so

$width^2+height^2= diagonal^2 \\{(\frac{4}{3} \times height)}^2+ height ^2=625 \\ \\\frac{25}{9} height^2=625 \\height^2= {225} \\height= 15 \\width=\frac{4}{3} \times 15=20$

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

$\frac{width}{height} =\frac{1.85}{1} \\ \\height= \frac{width}{1.85} =\frac{20}{1.85} =10.81\text{ inches}$

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