Altitude NT is drawn in right-angled triangle MNK with right angle N. Angle NMK = 12о. Find the corner TNK.

We are given a right-angled triangle MNK with a right angle N, that is, an angle MNK = 90 degrees. It is known that the height NT forms a right angle with the hypotenuse MK, since the height is a perpendicular. Hence the angle NTK = 90 degrees. Find the angle NKT in the triangle MNK, based on the theorem on the sum of the angles of the triangle:

180 – 90 – 12 = 72 degrees.

Now, using the same theorem, we find the unknown angle TNK in the triangle NTK:

180 – 90 – 72 = 12 degrees.

Answer: TNK angle = 12 degrees.