Constructing with only 2 amounts

[Masheroni]

Hi everybody,
I was shopping for a new TV and was taken aback when I realised that knowing the hypotenuse and the right angle of a triangle didn't allow me to determine the measurements of the entire thing. My maths skills aren't good enough to come up with the right equation but if you know an angle and a measurement and where that measurement is in relation to the angle, then shouldn't you be able to figure out the intercept points?

Please help me because I'm sure I'm wrong and I want to know why!

[Baltuilhe]

Good morning!

I think, in your TV case, that one more information is needed: the TV proportion size!
If you know that, you can calc the dimensions.
16:9 is a very popular proportion.

Let's see to a 47" (this is the diagonal, or the hypothenuse of a right triangle).
First, calc the diagonal size for the given proportion:

[tex]d^2=16^2+9^2=256+81=337\\d\approx 18,36[/tex]

So, if your TV is 16 (width) : 9 (height), the diagonal is 18,36.

You can calc, now, the width and height of you TV screen using a rule of three:

[tex]\dfrac{47}{18,36}=\dfrac{W}{16}=\dfrac{H}{9}\\
W=16\cdot\dfrac{47}{18,36}\approx 40,96\\
H=9\cdot\dfrac{47}{18,36}\approx 23,04[/tex]

I hope I have helped!