Question

How do you evaluate tan(π/3)?

Answer 1

`sqrt(3)`.

Explanation:

An equilateral triangle has all internal angles equal to `pi/3`.

Let's divide the triangle along its height in two. We obtain two rectangle triangles. The height of the triangle is the opposite catet and half of the side is the adjacent catet of the angle `pi/3`..

So `tan(pi/3)` is the `(height)/(half side)`.

To the detetermine the height we need to use the Pithagoras theorem:

`l^2=h^2+(l/2)^2`

`h^2=l^2-l^2/4=3/4l^2`

`h=sqrt(3/4)l=sqrt(3)/2l`

`tan(pi/3)=(height)/(half side)=(sqrt(3)/2l)/(l/2)=sqrt(3)`.