# Calcolare le dimensioni dei monitor16:9 a partire dalla diagonale

The shape of the modern flat-screen monitor, is close to that of cinema. From the old 4:3 format is passed to the most compelling aspect ratio of 16:9.

4:9 The two numbers indicate the ratio between the size of the base and height of the rectangle that displays the images. If the base is 16 inches, the height will be 9 inches. Clearly, these size increases if the screen is bigger, but they are always proportional.

Quickly to indicate the size of a television screen or monitor, is used to provide the length of the diagonal, in inches. Since the diagonal is possible to have an overall idea of the size of the screen, thanks to its rectangular shape and a fixed proportion between the base and height.

But how do you calculate these values? How do you get the actual size of the display surface of a widescreen TV?

The first thing to do is convert the length of the diagonal inches to centimeters. An Inch (known in English and indicated by two inch apicetti, type 23 "or 19") is equivalent to 2.54 cm exactly.

The formula is as follows (take as an example a 40”monitor):

1. Convert the diagonal (size) in inches from the monitor inches to centimeters:

40 * 2,54 = 101,6 cm

2. Divide the result by the constant 18.3576 to obtain the scale factor:

101,6 /18.3576 = 5,5344

3. Calculation of the largest side (b) of the monitor:

16*5,5344= 88,5504 cm

4. Calculation of the smaller side (a) of the monitor:

9*5,5344= 49,8096 cm

Our interactive display works on all types of screens a 4: 3 and 16:9

**Resolution of the issue through the Pythagorean theorem**

The Pythagorean Theorem relates the diagonal, and legs of a right triangle. If we denote by d the diagonal (hypotenuse) with base b and al’altezza, we have:

d^{2}=a^{2}+b^{2}

If we know one side (catheter) and the diagonal, we can calculate the other side with the Pythagorean Theorem. In our case we do not know either of the catheter, but we know that are proportional to the numbers 16 (catheter through) and 9 (cateto short).

Suppose we have a triangle with b = 16 cm and a = 9 cm. We apply the Pythagorean theorem and we get the diagonal d.

d= SQR(9^{2}+16^{2})= 18.3576

Our Standard Triangle, has a diagonal of 18.3576 (7.227 inches). We can use this bias, we call ds (diagonal standard) to determine the scaling factor for any diagonal.

Similarly we call the a_{s} and b_{s} with standard measures of a = 9 b = 16.

We obtain the scale factor by dividing the diagonal of our screen, with the value of the diagonal standard ds. We call this scale factor Rd to get the basic dimensions and height, multiply the sides by the factor b_{s} and a_{s} Rd

b= b_{s}*Rd

a= a_{s}*Rd

Considering a 23’’ monitor

d= 23″= 23*2.54= 58.42 cm (diagonal in centimeters)

Rd= d/ds= 58.42/18.3576= 3.1823 (scale factors)

b= 16*3.1823= 50.917 cm

a= 9*3.1823= 28.641 cm

So a monitor with diagonal 23 inches has a monitor of 51 x 29 centimeters.

Riassuming:

Rd= d/ds= d/18.3576

b= b_{s}*Rd= 16*Rd

a= a_{s}*Rd= 9*Rd

We could have same result using trigonometry

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