In triangle ABC, angle C = 90 degrees, height CD = √6, AD: DB = 2: 1. Find aircraft.

Let us prove the similarity of triangles АСD and ВСD.

Let the angle CBD = α0, then the angle BAC = (90 – α) 0. In a right-angled triangle ACD, the angle ACD = (90 – (90 – α)) = α0. Then the angle ACD = CBD, and the right-angled triangles ACD and BCD are similar in acute angle.

Let the length of the segment BD = X cm, then, by condition, the length of the segment AD = 2 * X cm.

From the similarity of triangles follows: CD / BD = AD / CD.

CD ^ 2 = BD * AD.

6 = 2 * X2.

X = √3 cm.

Then ВD = √3 cm.

By the Pythagorean theorem, in a right-angled triangle BCD, BC ^ 2 = CD ^ 2 + BD ^ 2 = 6 + 3 = 9.

BC = 3 cm.

Answer: The length of the BC side is 3 cm.