Given a triangle ABC, BM, AN- heights, AC = 42dm, BC = 35dm, BM = 28dm Calculate the height AN.

To begin with, let’s draw a triangle ABC, in which, according to the condition of the problem, we denote AC = 42 dm, BC = 35 dm, and BM = 28 dm.
Since the height AN falls on a known side, then in order to find this height, you need to find the area of the triangle.
Find the area of a triangle as the product of the height by the side divided by two.
Then the area is equal to: 28 * 42/2 = 588 dm2.
Then the height AN = 588 * 2/35 = 33.6 dm.