Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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? Triangle

Thank you, i don't have any trig basis.

share|cite|improve this question
An equilateral triangle can be cut into two 30-60-90 triangles. If $y$ is the altitude, then $x=\frac{y}{\sqrt 3}$. You can use the Pythagorean theorem for this: $y^2+x^2=4x^2$. – J. M. Jan 6 '12 at 16:31
You don't have enough information here. You need either one angle or the base length. – ja72 Jan 6 '12 at 16:40
@ja72,the triangle is equilateral. – leo Jan 6 '12 at 16:49
ja72, it's an equilateral triangle so all the angles are 60 deg. J.M. would you like to put that as an answer? so i can accept it? and thanks – André Alçada Padez Jan 6 '12 at 16:49
up vote 2 down vote accepted

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 $\tan 60°=\sqrt{3}$, $$x=\frac{y}{\sqrt{3}}.$$

share|cite|improve this answer
One thing I find problematic about this is that it assumes $\tan 60^\circ=\sqrt{3}$ rather than taking the opportunity to show how that fact is derived from the Pythagorean theorem. – Michael Hardy Jan 6 '12 at 20:19
@MichaelHardy: I was going off having "trigonometry" in the title; having your solution as well is certainly worthwhile (and +1 there). – Isaac Jan 6 '12 at 20:22

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 $$ y=\sqrt{(2x)^2-x^2} = \sqrt{4x^2-x^2}=\sqrt{3x^2}=x\sqrt{3}. $$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.