In a 30-60-90 triangle, the lengths of the sides are in a specific ratio:
- The side opposite the 30-degree angle is the shortest and is denoted as \(x\).
- The side opposite the 60-degree angle is \(x\sqrt{3}\).
- The hypotenuse is \(2x\).
In your case, the side opposite the 60-degree angle is given to be \(7\sqrt{3}\) cm. According to the ratio:
\[ x\sqrt{3} = 7\sqrt{3} \]
To find \(x\), we can divide both sides by \(\sqrt{3}\):
\[ x = 7 \]
Now, we can find the hypotenuse using the relationship \(2x\):
\[ \text{Hypotenuse} = 2x = 2(7) = 14 \text{ cm} \]
Thus, the hypotenuse is 14 cm long.