Which three pairs of measurements are possible side length for the triangle?

A, B, E, F

Step-by-step explanation:

In a 30-60-90 triangle, the hypotenuse is twice the length of the short leg.

That makes choice E possible.

In a 30-60-90 triangle, the long leg is sqrt(3) times the length of the short leg.

That makes choices A, B, and F possible.

First option.

Option 5.

Option 6.

Step-by-step explanation:

The formula for a 30-60-90 triangle is this:

1) Side opposite to 30 will be value .

2) Side opposite to 60 will be value .

3) Hypotenuse will be .

So let's look and see:

First option: and

AB is opposite of the angle with 30 degree measurement.

BC is opposite of the angle with 60 degree measurement.

So here.

So the side opposite of 60 using the formula should be which it is here.

So first option looks good.

Second option: and .

We aren't given the side opposite to 30.

AC is the hypotenuse so 2a=2 which means the side opposite to 30 is a=2/2=1.

This means using the formula that the side opposite to 60 will be but we don't have that.

So not option 2.

Third option: and

AB is the side opposite of 30, so we have

AC is the hypotenuse so that side should be and it isn't.

Option 3 is not working.

Fourth option: and

So we have that which means and so but that is a contradiction because we have this value should be 10.

Not option 4.

Option 5: and

So we have and so this looks good.

Option 6: and

so which is what we have.

Option 6 works.

go and ask your mom to you

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation: