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The question in the image asks you to find the remaining sides of a 30°-60°-90° triangle when the longest side (hypotenuse) is given as 11.

In a 30°-60°-90° triangle, the sides are in a specific ratio:
- The side opposite the 30° angle is \( \frac{1}{2} \) the hypotenuse.
- The side opposite the 60° angle is \( \frac{\sqrt{3}}{2} \) times the hypotenuse.
  
Given that the hypotenuse is 11:
1. The shorter leg (opposite the 30° angle) is \( \frac{1}{2} \times 11 = 5.5 \).
2. The longer leg (opposite the 60° angle) is \( \frac{\sqrt{3}}{2} \times 11 \).

Let's calculate the length of the longer leg.

The remaining sides of the 30°-60°-90° triangle are:
- The shorter leg (opposite the 30° angle) is \( 5.5 \).
- The longer leg (opposite the 60° angle) is approximately \( 9.53 \).

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you derive the side ratios for special triangles like the 30°-60°-90° triangle?
2. Can these ratios be applied to non-right triangles?
3. What other special triangles exist with fixed side ratios?
4. How would this problem change if the hypotenuse was not known?
5. What is the relationship between angles and side lengths in trigonometry?

**Tip**: Always remember that the hypotenuse is the longest side in any right triangle, and its length helps you easily calculate the other sides if you know the angles.

Find the remaining sides of a 30°-60°-90° triangle if the longest side (hypotenuse) is 11.

Learn how to find the remaining sides of a 30°-60°-90° triangle when the hypotenuse is 11. This problem involves understanding the ratio of sides in a special right triangle and applying formulas for the shorter and longer legs. Suitable for high school students.

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