Find a value of $\theta$ in the interval $[0^{\circ },{90}^{\circ }]$ that satisfies the given statement.
$$\cos \theta =0.87852455$$
$$\theta \approx$$
(Round to six decimal places if needed.)

Step 1 ：We are given the cosine of an angle and we need to find the angle itself. We can use the arccos function (also known as the inverse cosine function) to find the angle. The arccos function returns the angle in radians, so we will need to convert it to degrees.

Step 2 ：Given that $\cos \theta =0.87852455$

Step 3 ：Calculate the arccos of 0.87852455 to get the angle in radians: ${\theta }_{rad}=\arccos (0.87852455)=0.4980316258984871$ radians

Step 4 ：Convert the angle from radians to degrees: ${\theta }_{deg}={\theta }_{rad}\times \frac{180}{\pi }=28.535110228021615$ degrees

Step 5 ：Final Answer: The value of $\theta$ that satisfies the given statement is approximately ${\boxed{{\displaystyle 28.535110}}}^{\circ }$