In triangle ABC, angle B is straight, height BM = 12, AM = 16. Find MC.

Let us prove the similarity of right-angled triangles ABM and CBM.

Let the angle BAM = X0, then the value of the angle ABM = (90 – X) 0.

The angle ABC is straight, then in the triangle BCM the angle CBM = (90 – ABM) = (90 – (90 – X) = X0.

Then in right-angled triangles ABM and CВM the acute angles are equal, and therefore the triangles are similar.

Then AM / BM = BM / CM.

BM ^ 2 = AM * CM.

CM = BM ^ 2 / AM = 144 * 16 = 9 cm.

Answer: The length of the CM segment is 9 cm.