In triangle MNK MK = 8cm, MN = 6cm, angle M = 30degree, find side NK

We use the cosine theorem (the square of the side of a triangle is equal to the sum of the squares of the other two sides without the double product of these sides by the cosine of the angle between them).
a ^ 2 = b ^ 2 + C ^ 2-2b * c * cosa
In our problem NK opposite the angle М
NK ^ 2 = MK ^ 2 + MN ^ 2-2 * MK * MN * cosa
NK = √ (MK ^ 2 + MN ^ 2-2 * MK * MN * cosa)
NK = √ (64 + 36-2 * 6 * 8 * (√3 / 2)) = 4.1 cm.
Answer: NK = 41.