Question

What is the length of the hypotenuse of a 30-60-90 triangle if the side opposite the 60-degree angle is 6√3
?(1 point)
Responses

2√3
2 Start Root 3 End Root

12√3
12 Start Root 3 End Root

6
6

12

Answer 1

In a 30-60-90 triangle, the relationship between the lengths of the sides is as follows:

- The side opposite the 30-degree angle (shortest side) is \( x \).
- The side opposite the 60-degree angle (longer leg) is \( x\sqrt{3} \).
- The hypotenuse is \( 2x \).

Given that the side opposite the 60-degree angle is \( 6\sqrt{3} \), we can set up the equation:

\[
x\sqrt{3} = 6\sqrt{3}
\]

To solve for \( x \), divide both sides by \( \sqrt{3} \):

\[
x = 6
\]

Now, we can find the length of the hypotenuse:

\[
\text{Hypotenuse} = 2x = 2(6) = 12
\]

Therefore, the length of the hypotenuse is \( 12 \).

So, the correct answer is **12**.