Question

which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle?

Answer 1

There are many answers for a ratio question, and I do not know the choices but since each number could be divided by 30 I would. Do that to get 1:2:3. Hope this helps.

Answer 2

`√(3)` or
`(1)/(√(3) )`

Explanation:

There are no any options but we calculate the ratio of leg as the following way.

Construct a 30-60-90 triangle (ΔABC), which shown in the figure.

Let the length of one leg (AB) =
`x` units, then the length of the other leg (BC) of the triangle=
`BC=tan30*x` units

`BC =(1)/(√(3) ) *x` units

`BC=(x)/(√(3) )` units

Hence the ratio of legs in the triangle ABC is
`AB:BC = x:(x)/(√(3) ) =√(3)`

or the ratio of legs in the triangle ABC is
`BC:AB =(x)/(√(3) ) :x =(x)/(√(3) ) *(1)/(x)=(1)/(√(3) )`