this post was submitted on 19 Dec 2023
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Ratios can be used in trig -- if it's 1.5 times as long as it is tall, tan(\theta) = \frac{2}{3}, which then allows you to find the lengths of the other two sides easily so long as you have a calculator.
Right, but why bring theta into it at all? TV screens are as a hypotenuse (a²+b²) with a fixed ratio (a/b=16/9), so you just need to solve for a and b.
You don't have to, but it seems perfectly easy since you don't have to write anything down to solve it. c*sin(arctan(b/a)) gives b, and c*cos(arctan(b/a)) gives a. I'm not disputing that you can do it without, but I don't think it's necessarily any quicker or easier.
If it works it works. I just never would have thought to do it that way.