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

##sin(pi/3) = sqrt(3)/2##

Consider the series of diagrams below.

The interior angles of a triangle always add up to ##pi## radians

An equilateral triangle will have all three angles ##= pi/3## and all three sides of equal length.

If we set the sides of the equilateral triangle to ##2## we can avoid fractions when we divide the triangle into 2 halves vertically,

By , the height (the side opposite the angle of ##pi/3##) will have a length of ##sqrt(3)##

##sin(pi/3) = ("side opposite "pi/3)/("hypotenuse")=sqrt3/2##