Concept

Cosine

For an acute angle of a right triangle, the cosine of is the ratio between the lengths of the adjacent side and the hypotenuse.
Sides of a right triangle labeled
The cosine of is written as

While this trigonometric ratio expresses the ratio of the adjacent side to the hypotenuse, it does not state the actual measurements of their lengths.
Right triangle with two vertices movable and the cosine of one acute angle is computed while the measures change
It should be noted that for a given angle, when the adjacent side and hypotenuse lengths change, if their ratio stays the same, then the cosine, too, would stay the same.
Exercises