How do you evaluate tan(π/3)?

1 Answer
José F.
Mar 16, 2016

sqrt(3).

Explanation:

An equilateral triangle has all internal angles equal to pi/3.enter image source here

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).

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