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)
A. 6
B. 12 √ 3
C. 12
D. 2 √ 3

Answer 1

In a 30-60-90 triangle, the sides are in a specific ratio:

- The side opposite the 30-degree angle (shortest side) is \( x \).
- The side opposite the 60-degree angle 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 find \( x \), we can divide both sides by \( \sqrt{3} \):

\[
x = 6
\]

Now we can find the hypotenuse:

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

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

The correct answer is **C. 12**.