Question

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Explanation:

Step1: Identify trigonometric ratio

In right triangle \( ONM \), \( \angle O = 44^\circ \), hypotenuse \( ON = x \), adjacent side to \( \angle O \) is \( ON \)? Wait, no: \( \angle N = 90^\circ \), side \( ON \)? Wait, no, \( ON \) is hypotenuse? Wait, \( \angle N \) is right angle, so sides: \( ON \) is hypotenuse? Wait, \( \angle O = 44^\circ \), side \( ON \)? Wait, no, \( ON \) is length 9? Wait, the triangle has right angle at \( N \), so \( \angle N = 90^\circ \), \( \angle O = 44^\circ \), side \( ON \)? Wait, no, \( ON \) is length 9? Wait, \( ON \) is the hypotenuse? Wait, \( x \) is \( OM \), the hypotenuse? Wait, no, \( ON \) is length 9, \( \angle O = 44^\circ \), \( \angle N = 90^\circ \), so \( \cos(44^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{ON}{OM} \)? Wait, no, adjacent to \( \angle O \) is \( ON \)? Wait, \( \angle O \) is at vertex \( O \), so the sides: \( ON \) is adjacent, \( MN \) is opposite, and \( OM \) is hypotenuse (\( x \)). Wait, \( ON = 9 \), \( \angle O = 44^\circ \), so \( \cos(44^\circ) = \frac{ON}{OM} \), so \( OM = \frac{ON}{\cos(44^\circ)} \). Wait, no, \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \), so adjacent to \( \angle O \) is \( ON \), hypotenuse is \( OM = x \), so \( \cos(44^\circ) = \frac{9}{x} \), so \( x = \frac{9}{\cos(44^\circ)} \).

Step2: Calculate \( \cos(44^\circ) \)

Using calculator, \( \cos(44^\circ) \approx 0.7193 \).

Step3: Compute \( x \)

\( x = \frac{9}{0.7193} \approx 12.5 \) (rounded to nearest tenth).

Answer:

\( x \approx 12.5 \)