Find a value of $\alpha$ in $\left[0^{\circ}, 90^{\circ}\right]$ that satisfies the given statement. $\sec \alpha=1.3131199$ (Round to 6 decimal places)

Step 1 ：Given that \(\sec \alpha = 1.3131199\)

Step 2 ：We know that \(\sec \alpha\) is the reciprocal of \(\cos \alpha\), so \(\cos \alpha = \frac{1}{\sec \alpha} = \frac{1}{1.3131199} = 0.7615450805368192\)

Step 3 ：To find the value of \(\alpha\), we need to find the arccosine (inverse cosine) of \(\cos \alpha\). So, \(\alpha = \arccos(0.7615450805368192)\)

Step 4 ：The above value is in radians. To convert it to degrees, we multiply by \(\frac{180}{\pi}\). So, \(\alpha = 0.7051025675145597 \times \frac{180}{\pi} = 40.399401\) degrees

Step 5 ：Final Answer: The value of \(\alpha\) that satisfies the given statement is \(\boxed{40.399401^{\circ}}\)