16:9 n inch diag == width/height?

Factual Questions
1

If a TV has 16:9 aspect, and the diagonal size is n inches, what is the width/height of the picture?

It’s late, I’ve been fiddling in Excel for 30 minutes on this, and it’s really bugging me. I keep getting something like sqrt((diag*diag) * hiAspect )/loAspect. Not.
!@#!@ing Pythagoras :slight_smile:

2

h=n(sin(arctan(9/6)))

w=n(cos(arctan(9/16)))

http://www.jjgifford.com/expressions/geometry/trigonometry.html

or use h^2+w^2=n^2 and h/w=9/16

w=n/sqrt[(9/16)^2+1]

h=n/sqrt[(16/9)^2+1]

check my math, but the methodology is correct

3

So, if what you are saying is that the height is 9/16 of the width, then:

w= 16n (337)[sup]-1/2[/sup]

h=9n (337)[sup]-1/2[/sup]

4

Which is what John Mace Said…

Next time I’ll preview…

5

I hope I’m not presuming to translate for the slightly less geekily inclined.

For the height:
square the diagonal, divide by 4.16, then take the square root of the whole thing.

For the width:
square the diagonal, divide by 1.32, then take the square root of the whole thing.

It’s a close approximation using decimal conversions of the fractions, but it’s a lot easier with a basic pocket calculator and it comes out within a very small fraction of an inch.

6

Thanks, gang. I think John Mace’s second example was what I was going for, but thanks for the different approaches.

7

Talk about making things unnecessarily complicated. If the diagonal is n and the ratio is 16:9 then the sides are 0.87n and 0.49n

8

That’s what I said… I just like having all the decimal places.

Knowing the measurements to 1/10000 of an inch is important when trying to decide where to hang your plasma TV.

:wink:

9

>> Knowing the measurements to 1/10000 of an inch is important when trying to decide where to hang your plasma TV.

So why are you neglecting to take into account air temperature, pressure and humidity? :wink:

10

How do you derive that?

11

Let the sides be 16x and 9x and the diagonal be n. Use the Pythagorean theorem and solve for x in terms of n. Multiply x by 9 to get one side and by 16 to get the other. Since 337 is the sum of 9 squared and 16 squared,

0.49n = 9n/sqrt(337)
0.87n=16n/sqrt(337)

12

Or, looking at it another way: if one side of the rectangle is 16 and the other one is 9, then the diagonal is 18.36. Any screen with the same proportion will have proportional dimensions:



   n         a         b
------- = ------- = -------
 18.36      16         9

From where:

a = n * 16 /18.36
b = n * 9/18.36