Question 919540
The long side of a 30 60 90 triangle is twice as long as the short side,
so if there is no way to write the measure of the short side without a square root,
then there is no way to write the measure of the long side without a square root.
On the other hand,
maybe the measure of the medium length side will be an integer.
{{{drawing(450,200,-1.5,3,-0.5,1.5,
triangle(-1,0,0,0,-1,0.577),rectangle(-1,0,-0.9,0.1),
locate(-0.6,-0.02,1),locate(-1.15,0.45,sqrt(3)/3),
locate(-0.6,0.7,2sqrt(3)/3),locate(-0.5,0.21,30^o),
arc(0,0,1.1,1.1,180,210),
triangle(0.5,0,2.232,0,2.232,1),rectangle(2.232,0,2.132,0.1),
locate(1.3,-0.05,sqrt(3)),locate(2.25,0.55,1),
locate(1.3,0.7,2),locate(0.8,0.25,30^o),
arc(0.5,0,1.2,1.2,-30,0)
)}}}