While the cosine of a given angle is used to find the ratio of its opposite side / hypotenuse, the arccosine does the opposite: it finds the measure of an angle from the given ratio of its opposite side / hypotenuse.
For example, cos360∘(45∘)=√22
So cos360∘−1(√22)=45
So if you had the lengths of the opposite side and the hypotenuse for a right triangle, you would use arccosine to find the measure of the angle.
While the cosine of a given angle is used to find the ratio of its opposite side / hypotenuse, the arccosine does the opposite: it finds the measure of an angle from the given ratio of its opposite side / hypotenuse.
For example, cos360∘(45∘)=√22
So cos360∘−1(√22)=45
So if you had the lengths of the opposite side and the hypotenuse for a right triangle, you would use arccosine to find the measure of the angle.