In a 30-60-90 triangle, the side opposite the 30° angle has length 6. What is the length of the hypotenuse?

In a 30-60-90 triangle, the sides are in the ratio $1 : \sqrt{3} : 2$, where the shortest side is opposite the $30°$ angle, the longer leg is opposite $60°$, and the hypotenuse is opposite $90°$. The side opposite $30°$ is 6, so the hypotenuse is twice that: $2 \times 6 = 12$. Check with sine: $\sin 30° = \frac{1}{2} = \frac{6}{\text{hyp}}$, so the hypotenuse is 12. A common wrong answer is $6\sqrt{3} \approx 10.4$, which is the other leg. Another is 3, from halving instead of doubling. The hypotenuse is always the longest side.