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#### Nickoff

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Can someone please tell me what the width and height measurements are for 80, 90 and 100 inch diameter 16:9 screen sizes and also for 2.35:1 80, 90 & 100 inch diameter screens (I only went to school to eat my lunch.....).

Thanks.

#### John Kotches

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I think you mean Diagonal, not diameter. Most rectangular objects don't have diameters Next, I'm pretty sure those dimensions you gave are common screen widths not diagonals.

You're working with a right triangle here, so the pythagorean theorem is in effect. Assuming you're correct, for a 16:9 screen, the formula is

(16x)^2 + (9x)^2 = (diagonal)^2

256x^2 + 81x^2 = (diagonal)^2.

337x^2 = diagonal^2

Solving for an 80" diagonal, you have

337x^2 = (80)^2

337x^2 = 6400 (just use this formula for 16:9 screens all the time, I'm showing the work)

x^2 = 6400 / 337

x = 4.36"

So you know that the common unit is 4.36"

Width = 16x or 69.76" (basically 70")

Height = 9x or 39.24"

For a 2.35"1 screen, the pythagorean theorem is still in effect,

(2.35x)^2 + (x)^2 = (diagonal)^2

5.5225x^2 + x^2 = (diagonal)^2

Use this then:

6.5225x^2 = (diagonal)^2

Solving for an 80" diagonal, we'd have

6.5525x^2 = 80^2

x^2 = 6400 / 6.5525

x^2 = 976.76 (call it 977)

x = 31.26

Width = 2.35 * 31.26 or 73.46"

Height = 31.26

This checks out correctly If it's width, you just use width/16 (for 16:9 screens) and width / 2.35 (for 2.35:1) screens and solve.

For an 80" width, we have

80/16 = 5, so X = 5.

(16x)^2 + (9x)^2 = diagonal^2

80^2 + 45^2 = diagonal ^2

6400 + 2025 = diagonal^2

8425 = diagonal^2

91.78 = diagonal

For a 2.35:1 screen, x = 34.04

(2.35x34.04)^2 + (34.04)^2 = diagonal^2

(80)^2 + (34.04)^2 = diagonal^2

6400 + 1158.72 = diagonal^2

7558.72 = diagonal^2

86.94 = diagonal

Regards,

#### Strahan

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Wow, and to think all those kids who whine about how this-or-that math in math class won't help them out after school I didn't do so good in math, so I use http://www.projectorcentral.com/proj...calculator.cfm hehehe.

#### John Kotches

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Strahan,

This was a practical application of the work of Pythagorus I know there was a reason I paid attention in Geometry Class.

Regards,

#### Nickoff

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Thanks John.

I'm working with a limited width (approx. 80") for a screen and seeing if I can work something that would fit above my existing tv and hifi equipment storage unit in a family room situation. Now have to work out throw distances (thinking of coffee table set up. Wife won't let me hang anything from the ceiling....).

#### symiboy

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or simply,

For 16:9 screens:

Width = Diagonal divided by 1.15

Height = Diagonal divided by 2.04

For 2.35:1 screens:

Width = Diagonal divided by 1.087

Height = Diagonal divided by 2.554

For 4:3 screens:

Width = Diagonal divided by 1.25

Height = Diagonal multiplied by 0.6

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