Find a value of $\alpha$ in the interval $[0^{\circ },{90}^{\circ }]$ that satisfies the given statement.
$$\cot \alpha =1.2875262$$
(Round to 6 decimal places)

Step 1 ：The cotangent of an angle is the reciprocal of the tangent of the angle. Therefore, to find the angle whose cotangent is 1.2875262, we can take the reciprocal of 1.2875262 to get the tangent of the angle.

Step 2 ：$\cot \alpha =1.2875262$

Step 3 ：$\tan \alpha =\frac{1}{\cot \alpha }=\frac{1}{1.2875262}=0.7766832239996359$

Step 4 ：Then, we use the arctangent function to find the angle. The arctangent function returns the angle in radians, so we will need to convert it to degrees.

Step 5 ：${\alpha }_{rad}=\arctan (\tan \alpha )=\arctan (0.7766832239996359)=0.6603608158105972$

Step 6 ：${\alpha }_{deg}={\alpha }_{rad}\times \frac{180}{\pi }=37.835888$

Step 7 ：Final Answer: The value of $\alpha$ that satisfies the given statement is $\boxed{{\displaystyle {37.835888}^{\circ }}}$