Depending on the type of measurement, it either multiplies or divides the true value by the cosine of the angle between the two directions.
[1][2] Approximate error sizes for a few example angles are:[3] The error is equivalent to treating the hypotenuse and one of the other sides of a right-angled triangle as if they were equal; the cosine of the angle between them is the ratio[5] of their lengths.
[citation needed] Rather than measuring the desired vector (in this case, orthogonal width), the instrument is measuring the hypotenuse of a triangle in which the desired vector is in fact one of the legs.
[2][6][verification needed][better source needed] Thus the user might measure a block of metal and come away with a width of 208.92 mm when the true width is 208.91 mm, a difference that matters to the subsequent machining.
[2] If the instrument is very small, then optical alignment techniques can be used to reduce cosine error.