The height AM of triangle ABC divides its side BC into segments BM and MC. Find the segment MC if AB

The height AM of triangle ABC divides its side BC into segments BM and MC. Find the segment MC if AB = 10√2 cm, AC = 26 cm, ∠B = 45 °.

Consider the triangle ABM: angle M = 90 degrees (because AM is height), AB = 10√2, angle B = 45 degrees => BM = AM = x, according to the Pythagorean theorem we find AM: 100 * 2 = 2x ^ 2, x = 10. Consider the triangle AMC: angle M = 90 degrees, AM = 10, AC = 26, according to the Pythagorean theorem we find MS: 100 + MS ^ 2 = 676, MS = 24
Answer: 24