The height CD of right-angled triangle ABC, drawn from the vertex of the right angle

The height CD of right-angled triangle ABC, drawn from the vertex of the right angle, divides the hypotenuse AB into segments AD and DB. Find the AC leg if DB = 3.2 cm and AD = 1.8 cm.

Since triangle ABC is rectangular, and its height CD is drawn from the vertex of a right angle, then the square of its length is equal to the product of the segments into which CD divides AB.

CD ^ 2 = BD * AD = 3.2 * 1.8 = 5.76.

CD = 2.4 cm.

In a right-angled triangle ACD, we apply the Pythagorean theorem and determine the length of the hypotenuse AC.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 1.8 ^ 2 + 2.4 ^ 2 = 3.24 + 5.76 = 9.

AC = 3 cm.

Answer: The length of the AC leg is 3 cm.