Question

Which of the following could be the ratio of the length of the longer leg of a 30 60 90 triangle to the length of its hypotenuse

Answer 1

for 30 60 90 triangles, the ratio of the side lengths is
$\frac{1}{2} : \frac{ \sqrt{3} }{2} :1$
where the first is the shorter leg, the second is the longer leg, and the third is the hypotenuse (the longest side that doesn't form a 90 degree angle)

so the ratio of the longer leg to the hypotenuse is $\frac{ \sqrt{3} }{2} :1$
or
$\frac{ \frac{ \sqrt{3} }{2} }{1}$
which equals $\frac{ \sqrt{3} }{2}$