Question 620612
"In triangle ABC, angle A is a right angle, angle B measures 60 degrees."
So ABC is a 30-60-90 triangle (because {{{30^o}}}, {{{60^o}}}, and {{{90^o}}} are the angle measures).
If A is the right angle, then BC (opposite o angle A) is the hypotenuse.
AB and AC are legs of the right triangle.
Consider an equilateral triangle> It has three {{{60^o}}} angles and is split by each altitude into two congruent 30-60-90 triangles.9 (Call one of those angles, angle B).
In each of those right triangles, the short leg is half as long as the hypotenuse (BC), so for the smallest angle
{{{sin(30^o)=cos(60^o)=cos(B)=1/2}}}.
{{{cos(30^o)=sin(60^o)=sin(B)=sqrt(1-1/4)=sqrt(3/4)=sqrt(3)/sqrt(4)=sqrt(3)/2}}}.
And then, {{{tan(60^o)=sin(60^o)/cos(60^o)=(1/2)/(sqrt(3)/2)=1/sqrt(3)=sqrt(3)/3}}}