To find the length of side \( x \) given that \( \theta = 44^\circ \) and the height is 12, we can use trigonometric functions. Assuming \( x \) represents the length of the adjacent side to the angle \( \theta \), and the height (12) represents the opposite side, we can use the tangent function:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{12}{x} \]
Rearranging this formula to solve for \( x \), we have:
\[ x = \frac{12}{\tan(44^\circ)} \]
Now, calculating \( \tan(44^\circ) \):
\[ \tan(44^\circ) \approx 0.9657 \]
Now substituting this value back into our formula for \( x \):
\[ x \approx \frac{12}{0.9657} \approx 12.42 \]
Rounding to the nearest hundredth:
\[ x \approx 12.42 \]
Thus, the length of side \( x \) is approximately 12.42.
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