first of all, sorry for the lame question.
Having a starting point, A and a height (catet) of y, what's the formula to calculate x?
Thank you, i don't have any trig basis.
first of all, sorry for the lame question.
Having a starting point, A and a height (catet) of y, what's the formula to calculate x?
Thank you, i don't have any trig basis.
Since it's an equilateral triangle, each angle has measure 60°. If you consider one of the smaller, right triangles formed by the altitude, the legs have length $y$ (the altitude) and $x$ (along the base) and the angle opposite the $y$ leg has measure 60°, so \tan 60°=\frac{y}{x}. Since \tan 60°=\sqrt{3}, $x=\frac{y}{\sqrt{3}}.$
Use the Pythagorean theorem. The length of each side of the triangle is $2x$, so you have a right triangle (either the left half or the right half of the equilateral triangle) in which the hypotenuse has length $2x$ and one leg has length $x$. The height must therefore be $ y=\sqrt{(2x)^2-x^2} = \sqrt{4x^2-x^2}=\sqrt{3x^2}=x\sqrt{3}. $