Is it possible to calculate the ground of a triangle only using the height and top angle.

Click here to see a poorly draw sketch of what I'm trying to calculate.

So is it possible and how, to calculate exactly that, only using either regular math or geometry, trigonometry or vector math functions.

Answer - Thanks to peterwhy



Where the $60^\circ$ is the top angle and the $10$ is the height of the triangle.

  • $\begingroup$ No, the base is not fixed given the height and the opposite angle of base $\endgroup$
    – peterwhy
    Aug 15, 2013 at 7:12
  • $\begingroup$ What do I need more to be able calculate the desired result then? $\endgroup$
    – vallentin
    Aug 15, 2013 at 7:14
  • $\begingroup$ One base angle, or two other side lengths (but with two side lengths you don't even need to know the height) $\endgroup$
    – peterwhy
    Aug 15, 2013 at 7:27

1 Answer 1


Not possible, and I can give you two example triangles with same height ($10$) and same "top angle" ($60^\circ$) but with different base length.

Consider the equilateral triangle with all angles $60^\circ$. By trigonometry you can find the base length to be $\frac{20}{\sqrt 3} = \frac{20 \sqrt 3}{3}$.

However, if the triangle is instead a right-angled one, then the base length would be $10\sqrt3 = \frac{30\sqrt3}{3}$, 1.5 times longer than the previous case.

In fact, the base length can be made as long as you want, by having a base angle close to $180^\circ - 60^\circ$.

  • $\begingroup$ Thanks, that was exactly what I wanted. I edited my post and added the final math expression that I got from what you answered. $\endgroup$
    – vallentin
    Aug 15, 2013 at 7:54

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