In a 30°-60°-90° triangle, the sides have specific ratios. The relationship between the sides is as follows:

• The side opposite the 30° angle is the shortest side (let's call it $x$).
• The side opposite the 60° angle is $x\sqrt{3}$.
• The hypotenuse (opposite the 90° angle) is $2x$.

You mentioned that the "median side" is 6. It's important to note that in a 30°-60°-90° triangle, the median to the hypotenuse is half the length of the hypotenuse.

So, let's denote the hypotenuse by $2x$. The median to the hypotenuse is half of the hypotenuse, which gives:

$\frac{2x}{2} = x$

We are given that the median is 6, so:

$x = 6$

Now, we can find the remaining sides:

1. The shortest side (opposite the 30° angle) is $x = 6$.
2. The side opposite the 60° angle is $x\sqrt{3} = 6\sqrt{3}$.
3. The hypotenuse is $2x = 12$.

Thus, the remaining side (the side opposite the 60° angle) is $6\sqrt{3}$.

To summarize:

• The shortest side: 6
• The side opposite the 60° angle: $6\sqrt{3}$
• The hypotenuse: 12

Do you need more clarification or details about any part of the solution?

Here are some related questions:

1. How do you calculate the area of a 30°-60°-90° triangle?
2. What is the relationship between the median and the sides in other types of triangles?
3. How can you prove the side ratios for a 30°-60°-90° triangle using trigonometry?
4. What happens if the median side is not given in a 30°-60°-90° triangle?
5. How would you solve for missing sides in a 45°-45°-90° triangle?

Tip: Always remember that in a 30°-60°-90° triangle, the median to the hypotenuse is always half of the hypotenuse.