In a right-angled triangle KLM with a right angle K, a bisector MN is drawn, with NK = 13cm.

In a right-angled triangle KLM with a right angle K, a bisector MN is drawn, with NK = 13cm. Find the distance from point N to line LM.

Consider a right-angled triangle KLM with right angle K.

Let MN be the bisector of the angle M.

Drop the perpendicular NH from the point N to the line LM.

Obviously, the distance from point N to line LM is equal to NH.

Note that triangles MKN and MNH are rectangular.

Since MN is the bisector of the angle M, the angles KMN = HMN.

Therefore, triangles MKN and MNH are equal in hypotenuse and adjacent angle. Then NK = NH = 13 cm.

Answer: the distance from point N to line LM is 13 cm.