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The question asks you to order the sides of triangle ABC from longest to shortest. Given that triangle ABC is a right triangle, and we are provided with one of the angles, \( \angle B = 30^\circ \), we can use properties of right triangles to determine the relative lengths of the sides.

In any right triangle:
- The **hypotenuse** is always the longest side. In this case, the hypotenuse is **AC**.
- The side opposite the smaller angle (here \(30^\circ\)) is the shortest side. The side opposite \( \angle B = 30^\circ \) is **BC**.
- The remaining side, **AB**, is longer than BC but shorter than AC.

So, the correct order from longest to shortest is:
1. **AC** (hypotenuse)
2. **AB** (longer leg)
3. **BC** (shorter leg)

Thus, the correct answer is:
- **Option C: BC, AC, AB**

Would you like more details, or have any other questions?

Here are some related questions:
1. What is the significance of the 30-60-90 triangle in trigonometry?
2. How can we use trigonometric ratios to calculate side lengths in a right triangle?
3. What is the Pythagorean theorem, and how does it relate to right triangles?
4. How can we generalize the relationship between side lengths in right triangles?
5. Can we solve this triangle with exact values using trigonometric identities?

**Tip**: In a 30-60-90 triangle, the sides follow a specific ratio: \( 1 : \sqrt{3} : 2 \), with the hypotenuse being twice the shortest side.

Which list orders the sides of triangle ABC from longest to shortest length? (Right triangle, angle B = 30 degrees)

Learn how to order the sides of a right triangle from longest to shortest, given angle B = 30°. This problem involves properties of 30-60-90 triangles, commonly seen in geometry for students in Grades 7-10.

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