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- 11 Nov 14
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@ponderable saidYes, just Pythag.
I wonder why there are no takers.
The point is that you can apply Pythagoras with an additional boundary condition on the catheti.
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🙂
@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 saidThe y is squared not the 256
@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🙂
@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 saidTV screens are always supposed to be in the ratio 16:9 so the diagonal length is enough to describe the screen.
@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🙂
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🙂