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

Right triangle: width and height as your two legs, and the diagonal as your hypotenuse
You don't know the width and height but you know that they are in a 4:3 ratio. meaning the width is 4x and the height is 3x.

a^2 + b^2 = c^2
(4x)^2 + (3x)^2 = 25^2
16x^2 + 9x^2 = 625
25x^2 = 625
x^2 = 25
x = 5
so your TV width is 4x = 4*5 = 20 inches
your TV height is 3x = 3 * 5 = 15 inches

set up a proportion

width on movie. . . .......................width on TV
----------------------- = ---------------------
height on movie. . ......................height on TV


1.85 . . . ...........20
------- = ---------
. 1 . . . . ........h

1.85h = 20
h = 10.81

Answer 2

The choices are 13.51 in, 10.81 in, 15 in, and 8.12 inches

Answer 3

http://answers.yahoo.com/question/index?qid=20110221174722AAbdqbS

Answer 4

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
\[\frac{width}{height} =\frac{1.85}{1}\]
\[height= width/1.85\]
\[height= 20/1.85=10.25 inches\]
so movie will occupy a height 0f 10.256 inches on tv

Answer 5

Sorry made a mistake it'd be 10.81 inches

Answer 6

@penguinup did you understand the solution?

Answer 7

ok, thanks guys, I get it