If a TV's aspect ratio is 16:9 and I know the diagonal size of the screen, what formula is used to find width & height of the screen?
2007-12-26 14:42:20 · 10 answers · asked by mimajuem 1 in Science & Mathematics ➔ Mathematics
OK, now I remember. Been awhile since I had to use the Pythagorean theorem. Got it now and I've calculated the height & width of all the different TV sizes we're considering.
Thanks all.
2007-12-26 16:13:43 · update #1
Hi,
(16x)² + (9x)² = c² where c is the diagonal length
I hope that helps!! :-)
2007-12-26 14:49:29 · answer #1 · answered by Pi R Squared 7 · 0⤊ 0⤋
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RE:
If a TV's aspect ratio is 16:9 & I know the diagonal screen size. What formula is used to find width & height?
If a TV's aspect ratio is 16:9 and I know the diagonal size of the screen, what formula is used to find width & height of the screen?
2015-08-10 07:25:52 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Aspect Ratio Formula
2016-11-08 06:24:51 · answer #3 · answered by ? 4 · 0⤊ 0⤋
let w and h be the TV's width & height, then
w/h = 16/9
w = 16h/9
suppose the diagonal size, d is given
then
w^2 + h^2 = d^2
and
(16h/9)^2 + h^2 = d^2
h^2 ( 256/81 + 1) = d^2
(337/81) h^2 = d^2
h^2 = (81/337)d^2
h = √(81/337) d = 0.49d
w = (16/9)h = (16/9)0.49 d = 0.87d
2007-12-26 15:03:30 · answer #4 · answered by vlee1225 6 · 1⤊ 0⤋
the the ratio of length to height so you have a right triangletherefore to find the diagonal you use the Pythagoras theorem
c^2=a^2+b^2
c^2=16^2+9^2
c^2=256+81
c=sqrt(337)
c approx= 18.3576
2007-12-26 15:06:57 · answer #5 · answered by shadowca1964 4 · 0⤊ 0⤋
use the Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the lengths of two legs, and c is the length of the diagonal. Hence, for your problem: 5^2 + 3^2 = c^2 25 + 9 = c^2 34 = c^2 c = square root of 34 c = 5.83 - the length of the diagonal of your rectangle
2016-03-14 08:00:53 · answer #6 · answered by Anonymous · 0⤊ 0⤋
Does the ratio 3:4:5 ring a bell? Yup, the diagional in this ratio is "5" and 16 and 9 are squares of 3 and 4. hmmmm.
2007-12-26 15:03:13 · answer #7 · answered by cattbarf 7 · 0⤊ 0⤋
[07]
Let the length be 16x and the width or height be9x respectively
Now let us assume that the diagonal size be y units
(16x)^2+(9x)^2=y^2
256x^2+81x*2=y^2
437x^2=y^2
x^2=y^2/437
x=y/20.90
Hence if we know y i.e the diagonal length of the screen,the length of the TV wouuld be 16y/20.90 or0.7656y units and the height would be 9y/20.90 or 0.431y units
2007-12-26 14:58:52 · answer #8 · answered by alpha 7 · 0⤊ 1⤋
use these formulas:
width/height=aspect ratio
diagonal=sqrt(width^2+height^2)
2007-12-26 14:49:42 · answer #9 · answered by Lieutenant 1 · 0⤊ 0⤋
height = .49 * d
width = .87 * d
2007-12-26 14:46:34 · answer #10 · answered by Anonymous · 0⤊ 0⤋