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

Answer:

$\sqrt{3}$ or $\frac{1}{\sqrt{3} }$

Step-by-step 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

$BC =\frac{1}{\sqrt{3} } *x$ units

$BC=\frac{x}{\sqrt{3} }$ units

Hence the ratio of legs in the triangle ABC is $AB:BC = x:\frac{x}{\sqrt{3} } =\sqrt{3}$

or  the ratio of legs in the triangle ABC is $BC:AB =\frac{x}{\sqrt{3} } :x =\frac{x}{\sqrt{3} } *\frac{1}{x}=\frac{1}{\sqrt{3} }$