A little geometry/trig

So TV's come in diagonal measurements but using the ratio of sides can you calculate the dimensions of the set, height and width? So I think the ration is 16:9.
If the TV is a 75 inch diagonally, what would be the width and height?

I wonder why there are no takers.

The point is that you can apply Pythagoras with an additional boundary condition on the catheti.

@ponderable said
I wonder why there are no takers.

The point is that you can apply Pythagoras with an additional boundary condition on the catheti.

Yes, just Pythag.

If the ratio of the sides is 16 : 9, then each side must be 16 and 9 multiplied by the same constant (let's call it y)

By Pythag, (16y)^2 + (9y)^2 = 75^2

So 256y^2 + 81y^2 = 5625

337y^2 = 5625

y^2 = 5625/337 = 16.69

y= square root 16.69 = 4.1,

So your tv is 16 x 4.1 by 9 x 4.1 = 65.6 x 36.9 (inches)

@Blood-On-The-Tracks
Thanks, I wasn't sure how to tackle this one.

How did you get the second square?

So 256y^2 + 81y^2 = 5625

337y^2 = 5625

I get it, 16 squared is 256 but why the second squaring? I see 75^2 is 5625.

It's interesting you are doing the math using only half the screen🙂

@sonhouse
because Pythag states

a^2 + b^2 = c^2

c is the hypotenuse (the side opposite the 90 deg), a and b are the other 2 sides, in a 90 deg triangle

@Blood-On-The-Tracks
Yes, but it looks like the 256 is squared twice. Is that for real?

@sonhouse

No, it is added to the 81 (9^2)

It's not rocket science, my friend

@Blood-On-The-Tracks
This is true but it looks like you have 256 squared again. Of course that would be a bit too large🙂 65536, a familiar number in early comps🙂

@sonhouse said
@Blood-On-The-Tracks
This is true but it looks like you have 256 squared again. Of course that would be a bit too large🙂 65536, a familiar number in early comps🙂

The y is squared not the 256

@AThousandYoung
Ah, I thought that would have been 256*(y^2) That would have cleared it up for me. Thanks for your help on this little problem. I was thinking about those TV sets where they always give the diagonal not up down and left right, is there a constant you could multiply the diagonal measure to any number? Seems reasonable there should be a straight line nice and linear. Right now I am working on my homage to my dear departed friend George Winston and writing tunes in his honor, have three or four on Soundcloud now. We were friends from when we both lived in Venice Beach back in the 70's. Haven't done much math lately🙂

@sonhouse said
@AThousandYoung
Ah, I thought that would have been 256*(y^2) That would have cleared it up for me. Thanks for your help on this little problem. I was thinking about those TV sets where they always give the diagonal not up down and left right, is there a constant you could multiply the diagonal measure to any number? Seems reasonable there should be a straight line nice and ...[text shortened]... re friends from when we both lived in Venice Beach back in the 70's. Haven't done much math lately🙂

TV screens are always supposed to be in the ratio 16:9 so the diagonal length is enough to describe the screen.

So if h=height, w= width, and d=diagonal,

h^2 + w^2 = d^2

(9/16 * w)^2 + w^2 = d^2

@AThousandYoung
And of course double the area of each triangle, if you were going for area🙂