The **cosine** of the angle M (in a right triangle Mnl) is one of the three calculated **trigonometric ratios** of the angle. The cosine value can be calculated using the length of the sides of the right triangle. To get the value of cos M, we must first find the length of the sides of the right triangle Mnl, then we can use the **Cosine Rule**.

The Cosine Rule states that: *cos M = a² + b² – c² / 2ab*, where a is the length of Ml, b is the length of Mn and c is the length of nl.

For example, if the right triangle Mnl has sides of 5, 12 and 13, then the calculation will be:

cos M = (5² + 12² – 13²) / (2 * 5 * 12)

cos M = (25 + 144 – 169) / (10 * 12)

cos M = 10 / 120

cos M = 0.0833

Therefore, the value of cos M in this case is 0.0833.

It is important to note that the Cosine Rule only works for right-angled triangles, and the lengths of the sides must be known before the value of cos M can be calculated.

If the lengths of the sides are not known, then another method must be used to calculate the value of cos M. This could include using the **Law of Cosines**, or using other trigonometric functions such as sine or tangent.