Which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle? check all that apply.

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second. So, in this case our numbers are the two legs of a triangle. Given that this is a right triangle because one angle is equal to 90, the the relations are as follows:




In the figure below α = 30, so




There are two ratios:

and

 

Therefore:

 

 

Finally, matching these results with the image above, the ratio:



is the only one that apply