Question

You have purchased a 42 inch television with an aspect ratio of 16:9. You want to watch a movie which has an aspect ratio of 1.85:1. Find the following measurements & show all work:

1. Height of the television screen

2. Width of the television screen




3. Height of the black bars at the top and bottom of the screen.





4. Percent of the area of the television screen that is covered by the image.

Answer 1

what a pain, but i think we can do it

Answer 2

if you recognize the hidden \(3:4:5\) triangle in the question, you can go right to the answer for the first one, but we can do the work anyway
since the ratio is \(16:9\) we can call one side length \(9x\) and the other side will be \(16x\)
then use pythagoras

Answer 3

hmmm maybe i don't know what "aspect ratio" means, i thought this was going to be snappy, but maybe i made a mistake
do you know what aspect ratio means, or should i look it up?

Answer 4

http://en.wikipedia.org/wiki/Aspect_ratio_%28image%29
ok we have to do some work
\[(16x)^2+(9x)^2=42^2\]
\[337x^2=42^2\]
\[x^2=\frac{42^2}{337}\]
\[x=\frac{42}{\sqrt{337}}\] so dimensions are
\[\frac{16\times 42}{\sqrt{377}}\] and
\[\frac{9\times 42}{\sqrt{337}}\]

Answer 5

a calculator will improve this answer probably

Answer 6

height is \(20.59\) and width is \(36.6\) to two decimal places