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

`(1)/(2) : ( √(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
`( √(3) )/(2) :1`
or

`( ( √(3) )/(2) )/(1)`
which equals
`( √(3) )/(2)`