Question

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

Answer 1

E. 1 : square root 3

F. Square root 3 : 3

Explanation:

Answer 2

E and F.

Explanation:

Let the side opposite the smallest angle have a measurement of x (this is the shortest side).

The hypotenuse is twice the shorter side so the hypotenuses would be 2x in this case.

The long leg is square root of 3 times the short side or sqrt(3)x in this case.

So the ratio of long leg to short leg is
`(√(3)x)/(x)=sqrt(3):1`

and

the ratio of short leg to long leg is
`(x)/(√(3)x)=1:sqrt(3)`.

The answer is not A that division is equivalent to 1:1.

B same reason as A.

C is not right because 1:sqrt(2) is not the same as 1:sqrt(3)

I bolded the reason in C so you can see why I said that.

You can also put these in your calculator and compare the decimals like so:

D gives us 0.816 approximately while sqrt(3)/1 gives 1.73 and 1/sqrt(3) gives 0.58 approximately. 0.816 is neither one of those.

How about E? 1:sqrt(3) is exactly what one of our ratios say.

How about F? sqrt(3)/3=0.58 so this is what one of our ratios is equivalent to.

So E and F are your answers.