Definition: In a right triangle, the cosine of an acute angle is the length of the side adjacent to that angle divided by the length of the hypotenuse.
What does cosine measure?
For an acute angle A, cos A = adjacent / hypotenuse. The adjacent side is the leg that touches the angle, not the hypotenuse. Like sine, the ratio depends only on the angle.
What is the link to sine?
In a right triangle, the sine of one acute angle equals the cosine of the other, because the opposite side of one is the adjacent side of the other. So sin 25 degrees = cos 65 degrees.
Example. A ladder 6.4 m long leans against a wall and makes a 70 degree angle with the ground. The distance from the wall to the foot of the ladder is the adjacent side: 6.4 · cos 70 degrees. Since cos 70 degrees is about 0.3420, the distance is about 2.19 m.
What goes wrong?
Mixing up which leg is adjacent, or using cosine when the known side is opposite. Another error is entering the angle with the calculator set to radians. If you need an angle, use cos-1. For an acute angle the cosine is between 0 and 1.