\( 1 \leftarrow \quad \) Find a value of \( \alpha \) in the interval \( \left[0^{\circ}, 90^{\circ}\right] \) that satisfies the given statement. \( \cot \alpha=1.2199536 \)

To find the value of \( \alpha \) that satisfies \( \cot \alpha = 1.2199536 \), we can use the fact that \( \cot \alpha = \frac{1}{\tan \alpha} \). Therefore, we can find \( \tan \alpha = \frac{1}{1.2199536} \), which is approximately \( 0.819 \). Using a calculator or a trigonometric table, the angle \( \alpha \) that corresponds to a tangent value of \( 0.819 \) falls in the first quadrant. The value of \( \alpha \) is approximately \( 39.6^{\circ} \).