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This is a problem involving a 30-60-90 right triangle, a special type of triangle with fixed ratios between its sides. In such triangles:

- The side opposite the 30° angle (the short leg) is \( x \).
- The side opposite the 60° angle (the long leg) is \( x\sqrt{3} \).
- The hypotenuse (opposite the 90° angle) is \( 2x \).

In this problem, you're given the short side (opposite the 30° angle), which is 4.4. We need to determine the length of the long leg, opposite the 60° angle.

### Step-by-step solution:

1. **Identify the given value**:  
   - Short leg = \( x = 4.4 \)

2. **Apply the ratio for the long leg**:  
   The long leg is \( x\sqrt{3} \).  
   Substituting the value of \( x \):  
   \[
   \text{Long leg} = 4.4 \times \sqrt{3}
   \]

3. **Calculate**:  
   \[
   \text{Long leg} = 4.4 \times 1.732 \approx 7.6
   \]

### Final Answer:
The length of the long leg is approximately **7.6 units** (rounded to the nearest tenth).

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Would you like more details on any part of this solution? Here are five related questions that expand on this concept:

1. How do you calculate the hypotenuse in a 30-60-90 triangle?
2. What are the general properties of special right triangles?
3. How can you derive the ratios for a 30-60-90 triangle from an equilateral triangle?
4. What are some practical applications of 30-60-90 triangles in real life?
5. Can you solve for all sides if the hypotenuse is known in a 30-60-90 triangle?

**Tip**: Memorizing the side ratios of special triangles, like 30-60-90 and 45-45-90 triangles, can save you a lot of time in geometry problems.

Determine the length of the long leg of a 30-60 right triangle if the short side is 4.4.

Learn how to calculate the long leg of a 30-60-90 triangle when the short side is 4.4. Using the special right triangle ratios, the long leg equals 4.4 * sqrt(3), approximately 7.6. Suitable for students in Grades 7-10.

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