Question

A movie that was shot with an aspect ratio of 2.35:1 is going to be shown on a 60-inch, wide screen television with an aspect ratio of 16:9.

What is the height of the image?

What is the height of the black borders for the letterbox view?

What percent of the screen’s area is being used to show the movie?

Answer 1

Solution-

Since a movie was shot with an aspect ratio of 2.35:1

So, width : height (of the movie shot )= 2.35 : 1

If it is going to be shown on a 60-inch, wide screen television with an aspect ratio of 16:9.

Ir means, width : height (for screen) = 16 : 9

Let the width of the screen be 16x .So, it's height must be 9x.

So, width of screen = 16x = 60 inch .....(1)

This implies x = 60/16 = 3.75 inch

So, height of the screen =9x = 9(3.75) = 33.75 inch ...(2)

Now,

(a)

Let height of the image be y inch then the width of the image is 2.35y inch.(Aspect ratio of shoot = 2.35 :1 )

Since width of the image = width of the screen

So, 2.35y = 60 inch (from equation 1)

Or y = 60/2.35 =25.53191489 inch

So, height of the image = 25.53191489 inch

Hence, the height of the image is 25.53 inch

(b)

Since height of screen is 33.75 inch (from equation 2)

and height of the image is 25.53 inch (as calculated above).

So,

33.75 - 25.53 =8.22 inch of screen is black.

So, The height of the black borders for the letterbox view is 8.22/2 = 4.11 inch (both at top and at bottom)

Hence, height of the black borders for the letterbox view is 4.11 inch.

(c)

Since width of the screen is 60 inch and height of the screen is 33.75 inch.

So, area of the screen

As= height×width = 33.75×60 = 2025 squares inches

Since width of image is 60 inch and height of image is 25.23191489 inch.

So, Area of the screen used to show movie =

Am=height×width

=25.23191489×60 =1531.9 square inches

Now, percentage of the screen’s area used to show the movie is

=(Am/As)×100

=(1531.9/2025)×100

75. 65%

Hence, 75.65 % of the screen's area is used to show the movie.