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The problem is asking for the missing side \( x \) in a right triangle, where the angle opposite \( x \) is \( 31^\circ \), and the given side adjacent to the angle is 12. Let’s solve it step by step:

### Step 1: Identify the relationship
Using trigonometry, we know:
\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\]
Here:
- Opposite = \( x \) (the missing side)
- Adjacent = \( 12 \)
- Angle = \( 31^\circ \)

So:
\[
\tan(31^\circ) = \frac{x}{12}
\]

### Step 2: Solve for \( x \)
Rearranging:
\[
x = 12 \cdot \tan(31^\circ)
\]

### Step 3: Calculate
Using a calculator:
\[
\tan(31^\circ) \approx 0.6009
\]
\[
x = 12 \cdot 0.6009 = 7.211
\]

### Step 4: Round to the nearest tenth
\[
x \approx 7.2
\]

### Final Answer:
The missing side \( x \) is approximately **7.2**.

Let me know if you’d like further clarification! 

Here are 5 related questions to deepen your understanding:
1. What trigonometric function would you use if the hypotenuse and one angle were given instead?
2. How would you calculate the hypotenuse in this triangle?
3. What are the sine and cosine values for the \( 31^\circ \) angle?
4. How does rounding impact real-world applications of these calculations?
5. Why is it essential to know which side is opposite, adjacent, or the hypotenuse?

**Tip:** Always double-check which trigonometric ratio (sine, cosine, tangent) fits the problem based on the given sides.

Find the missing side. Round to the nearest tenth. In a right triangle, the angle opposite x is 31°, and the adjacent side is 12.

Learn how to calculate the missing side of a right triangle using the tangent function. Given a 31° angle and an adjacent side of 12, this step-by-step solution shows how to find the opposite side and round to the nearest tenth. Perfect for high school trigonometry students.

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