Equations for 16:9 rectangle driven by diagonal dimension 1

[cinnamongirl]

May be I'm being too quick on the trigger by posting this question here.

I'm trying to create a sketch of a rectangle that has a 16:9 ratio (yes, a widescreen, you guessed correctly). I want to add equations to the width and height to maintain the 16:9 ratio, but I want to the size of the rectangle to be driven by a diagonal dimension. Any suggestions?

 

[cinnamongirl]

One solution I just tried was dimensioning the diagonal "construction" line and the angle between that line and one of the sides (after creating a 16:9 ratio rectangle). It seems to work, but I'd like a more "scientific" method using equations.

 

[JohnRBaker]

You mean something like the Pythagorean theorem ;-)

John R. Baker, P.E.
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[ctopher]

http://answers.yahoo.com/question/index?qid=20080803061719AACh53S

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[JohnRBaker]

Attached is an Excel spreadsheet with the formulas already worked out for you. Enter a 'Diagonal' and it will give you the Height and Width of a 16:9 (widescreen) rectangle.

Since I'm NOT a SolidWorks user you'll have to figure out how these formulas would be formatted in order to define your 'sketch'.

Have fun ;-)

John R. Baker, P.E.
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Product Engineering Software
Siemens PLM Software Inc.
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http://www.siemens.com/plm

UG/NX Museum:

http://www.plmworld.org/p/cm/ld/fid=209

To an Engineer, the glass is twice as big as it needs to be.

 

[TheTick]

You're trying too hard. Just make a rectangle that is 16:9, draw a diagonal, and add an angular dimension from the diagonal to any side. This will maintain the 16:9 ratio and allow you to stretch and resize and control size with only one dimension (even diagonal).

Honesty may be the best policy, but insanity is a better defense.

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[rollupswx]

Once you have it set up you can read off the horizontal and vertical dimensions from reference (driven) dimensions given the diagonal (driving) dimension.

 

[JohnRBaker]

But cinnamongirl stated that she didn't WANT to use the constraint angle method, which she acknowledged was possible, but rather work it out using "...a more "scientific" method using equations." Thus my spreadsheet example, complete with a "scientific" method ;-)

John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA

http://www.siemens.com/plm

UG/NX Museum:

http://www.plmworld.org/p/cm/ld/fid=209

To an Engineer, the glass is twice as big as it needs to be.

 

[cinnamongirl]

Well, my hope was that there would be an easy equation like X is the width, and Y (the height) is always 9/16 of X, even if X is not defined.

I suppose I could use the figures in JohnRBaker's spreadsheet to create equations between the sides' and the diagonal construction line's dimensions, but I think I'm going to stick with using the angle for now. Thanks to everyone for your help.

 

[JohnRBaker]

Well just remember, geometry is what it is...

I'll challenge anyone to come-up with a simpler 'equation-based' solution than what I proposed. That being said, are you suggesting now that you're NOT interested in having the Diagonal distance as being the only variable? After all (from your initial post)...

I want to add equations to the width and height to maintain the 16:9 ratio, but I want to the size of the rectangle to be driven by a diagonal dimension.

John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA

http://www.siemens.com/plm

UG/NX Museum:

http://www.plmworld.org/p/cm/ld/fid=209

To an Engineer, the glass is twice as big as it needs to be.

 

[TheTick]

Deliberately making a problem more complicated is not "scientific".

 

[TheTick]

Height = sin(arctan(9/16)) * diagonal

Apply appropriate SW syntax to the above equation. Pat yourself on the back for being more "scientific".

 

[cinnamongirl]

TheTick, thanks that equation worked (except I applied it to the width, not the height).

I hope we all learned something from this thread because I think I may end up using the angular dimension solution after all. We paid so much for SolidWorks, might as well take advantage of its powerful tools.

 

[EEnd]

w = 16 * d / sqrt(337)
h = 9 * d / sqrt(337)

That said, I would not use equations. I would draw small horizontal and vertical segments to make a small triangle with the diagonal to establish the slope for 16x9.

Eric

 

[drawoh]

cinnamongirl,

Draw the rectangle sides as line segments. Do 16 on the bottom, and 9 on the sides.

JHG

 

[DiegoLGraves]

I love word problems! Is this plasma or lcd? Where are the speakers mounted? How large is the bezel? Table or wall mount?

Sorry, a little shaky from a late lunch. Diego