# How do I evaluate tan(pi/3) without using a calculator?

Apr 8, 2018

Look at a $1$, $\sqrt{3}$, $2$ right angled triangle to find:

$\tan \left(\frac{\pi}{3}\right) = \sqrt{3}$

#### Explanation:

Note that $\frac{\pi}{3}$ is the internal angle of an equilateral triangle.

If we bisect an equilateral triangle with side length $2$, then we get two right angled triangles, each with sides $1$, $\sqrt{3}$ and $2$.

Hence we find that:

$\tan \left(\frac{\pi}{3}\right) = \text{opposite"/"adjacent} = \frac{\sqrt{3}}{1} = \sqrt{3}$