Answer:
E and F.
Step-by-step 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 [tex]\frac{\sqrt{3}x}{x}=sqrt(3):1[/tex]
and
the ratio of short leg to long leg is [tex]\frac{x}{\sqrt{3}x}=1:sqrt(3)[/tex].
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.
