The height of a right-angled triangle drawn from the vertex of the right angle divides the hypotenuse

The height of a right-angled triangle drawn from the vertex of the right angle divides the hypotenuse into segments 2 and 18 find this height

Since CH is the height of triangle ABC, triangles ACH and BCH are rectangular. Let us prove the similarity of triangles ACH and BCH.

Let the value of the angle HAC of the triangle ABC be equal to X0, then the angle ACH = (90 – X) 0.

Angle АСВ = 90, then angle ВСН = (90 – (90 – X) = X0.

The acute angles of the right-angled triangles ACH and BCN are equal, then the triangles are similar in acute angle.

Then in similar triangles AH / CH = CH / BH.

CH2 = AH * BH = 18 * 2 = 36.

CH = 6 cm.

Answer: The length of the CH height is 6 cm.