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

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Answer 1 · 2018-04-08T00:04:07

Look at a $1$ , $sqrt(3)$ , $2$ right angled triangle to find:

$tan(pi/3) = sqrt(3)$

Note that $pi/3$ 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 $2$ .

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Hence we find that:

$tan(pi/3) = "opposite"/"adjacent" = sqrt(3)/1 = sqrt(3)$

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