To find the length of side \( x \) given that one side measures \( 12 \) and the angle \( \theta \) is \( 44^\circ \), we need to know the context in which these measurements are provided.
Assuming you are dealing with a right triangle where:
- \( 12 \) is the length of the adjacent side to angle \( \theta \), and
- \( x \) is the opposite side,
You can use the tangent function, which is defined as:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
Thus,
\[ \tan(44^\circ) = \frac{x}{12} \]
To find \( x \), rearrange the equation:
\[ x = 12 \cdot \tan(44^\circ) \]
Now, we can calculate this value. First, find \( \tan(44^\circ) \):
Using a calculator:
\[ \tan(44^\circ) \approx 0.9657 \]
Now plug this value into the equation:
\[ x = 12 \cdot 0.9657 \approx 11.5884 \]
Now round to the nearest hundredth:
\[ x \approx 11.59 \]
Thus, the length of side \( x \) is approximately \( \boxed{11.59} \).
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