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The question asks to identify the correct set of side lengths for a 30-60-90 right triangle. 

For a 30-60-90 triangle, the ratio of the side lengths is always:
- The shortest side (opposite the 30° angle) = \( x \)
- The longer leg (opposite the 60° angle) = \( x \sqrt{3} \)
- The hypotenuse = \( 2x \)

Now, let's analyze each option:

- **A. \{5, 10, 10√3\}**: This option does not follow the correct ratio of 1:√3:2. The hypotenuse is not twice the shorter leg.
- **B. \{5, 5√3, 10\}**: This follows the correct ratio. Here, \( x = 5 \), the longer leg is \( 5\sqrt{3} \), and the hypotenuse is \( 2(5) = 10 \). This is the correct answer.
- **C. \{5, 5√2, 10\}**: The longer leg is incorrectly given as \( 5\sqrt{2} \), which does not fit the 1:√3:2 ratio.
- **D. \{5, 10, 10√2\}**: Similar to option A, this does not follow the correct side ratio.

Thus, the correct answer is **B**.

Would you like more details on how 30-60-90 triangles work or further clarifications?

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Here are some related questions for practice:
1. What are the side ratios for a 45-45-90 triangle?
2. If the shortest side of a 30-60-90 triangle is 7, what are the other two sides?
3. How does the Pythagorean theorem confirm the side lengths of a 30-60-90 triangle?
4. What are the key characteristics of special right triangles?
5. How would you apply 30-60-90 triangles in real-world problems?

**Tip:** For 30-60-90 triangles, always start by identifying the shortest side. The other two sides can be derived by simple multiplications.

Which set of values could be the side lengths of a 30-60-90 triangle?

Learn how to identify the correct side lengths of a 30-60-90 triangle, following the side ratio rule of 1:√3:2. This problem covers key geometry concepts and special right triangles. Suitable for students in Grades 9-11.

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