Math Help - Deriving a generic formula:

1. Deriving a generic formula:

Hello MHF community,

For my first post to this website, leave it to me to ask a very silly question. I am going to write what I know (which is incorrect). I am just missing some basic rules on how to solve equations to make it work, and I am hoping you can fill it in.

I am trying to derive a generic formula for finding the altitude for an equilateral triangle. I know this:

I know this is incorrect because when I graph the equilateral triangle, the height of the point does not fall where my formula suggests it will. So I went looking on the internet to find what I was doing wrong. However, the internet has just the answer to my question. Not the reason why my formula is wrong. Can you please help?

2. You forgot to square (x/2), and I'm not sure how you did the last step. Also the line on the radical sign doesn't extend over the x in the second-to-last-line, don't know if that was intentional.

Should be

$a = \sqrt{x^2-\left(\frac{x}{2}\right)^2}$

$a = \sqrt{x^2\left(1-\frac{1}{4}\right)}$

$a = x\sqrt{\frac{3}{4}}$

$a = \left( \frac{\sqrt{3}}{2}\right)x$

Edit: By the way, hello and welcome to Math Help Forum!