Calculating size of widescreen tv

[Ric]

If a widescreen TV size is given as: 32" I have calculated that the width
and height are approximately: 15.5" x 27.5"

That's presuming that the 32" diagonal measurement is 'visible screen' and
that the aspect ratio is 1:1.77

Can someone help me with a general purpose formula to accurately work out
height and width of a rectangle based on diagonal measurement and ratio of
sides?

Thanks

Ric

 

[James Silverton]

If a widescreen TV size is given as: 32" I have calculated that the width
and height are approximately: 15.5" x 27.5"

That's presuming that the 32" diagonal measurement is 'visible screen' and
that the aspect ratio is 1:1.77

Can someone help me with a general purpose formula to accurately work out
height and width of a rectangle based on diagonal measurement and ratio of
sides?

Do you remember Pythagoras' theorem and simultaneous equations? (g)

Jim.

 

[Ric]

Yep - so the square of the diagonal is equal to the square of the other two
sides, still need to split the resulting figure to the ratio 1:1.77 - I'm
sure this is bleedin' obvious too... but help would be appreciated!

Ric

 

[Ken Wright]

Diagonal (32) = d, so diagonal squared = d^2

Ratio of Height (h) to width (w) = 1:1.77, so if height = h, then width = 1.77h

Pythagoras tells us that h^2 + w^2 = d^2, so =>

(1.0)h^2 + (1.77h)^2 = d^2

Expanding the data in the brackets =>

(1.0 * h^2) + (1.77^2 * h^2) = d^2 =>

1.0h^2 + 3.1329h^2 = d^2 =>

4.1329h^2 = d^2 =>

h^2 = d^2 / 4.1329 (d=32) =>

h^2 = 1024 / 4.1329 =>

h = 15.74 =>

w = 1.77h =>

w = 1.77 * 15.74 = 27.86

 

[Kempy]

A1 input screen size ie. 32
A2 =((A1^2)*256/337)^0.5
A3 =((A1^2)*81/337)^0.5

 

[Ric]

Thanks Ken

So:

Where Diam (B1) = 32
Height [=SQRT(B1^2/4.1329)] = 15.74
Width [=1.77*B2] = 27.86

It's interesting that Boxclever (TV Rental Company) gave the measurements of
a 32" screen (their website uses metric) as Width=26 and Height = 15. So
its either sloppy use of a tape measure or the screen Diameter given isn't
accurate, perhaps like monitors - visible area is less.

======================================================

 

[Ric]

Thanks Kempy

Kens formula produces: 32 diam - 27.86 width - 15.74 height
Your formula produces: 32 diam - 27.89 width - 15.69 height

Both 100% correct according to Pythagoras - but Ken's is 100% accurate for
ratio too.

Both round to: 32 - 27.8 - 15.7 which is accurate enough for my purpose!

Big thanks to both of you for answering - I find this the most helpful
newsgroup to ask for help...

Ric

====================================

 

[Earl Kiosterud]

Ric,

Using trig to solve this, the angle of the diagonal is
=ATAN(9/16)

The relationship of the height or width to the diagonal is given by Sin and
Cos. Since we now know the angle, we plug it in:

Height: Diagonal*SIN(ATAN(9/16))
(15.6883596682419 for diag =32)
Width: Diagonal*COS(ATAN(9/16))
(27.8904171879856 for diag = 32)

Of course this is only out to 15 decimal places. Close enough for
commercial work, I'd think. This won't tally with measured height and width
because of the way the manufacturer measures the diagonal. It's the
diagonal of the CRT, out of the cabinet, not the inside of the bezel around
it (the actual viewable diagonal). And they probably measure around to the
side halfway to the back of the durned tube too. Manufacturers are wacko
with numbers, because we buy them (figuratively AND literally). <g> Once
one manufacturer stretches a number, the others must do so, or they lose.

Earl Kiosterud
mvpearl omitthisword at verizon period net

 

[Ric]

Thanks Earl - another interesting response! Very true about manufacturers
number skills, amazing that Boxclever use Metric on their website and
Imperial in their shops!?

Ric