In a right-angled triangle ABC with a right angle C, the height CD is drawn.

In a right-angled triangle ABC with a right angle C, the height CD is drawn. It is known that AD = 3.2 cm, AC = 4 cm. Find the unknowns, the sides of the triangle ABC.

In a right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the height CD.

CD ^ 2 = CA ^ 2 – AD ^ 2 = 16 – 10.24 = 5.76.

CD = 2.4 cm.

The height of CD is drawn at the hypotenuse of CD, then CD ^ 2 = AD * BD.

BD = CD ^ 2 / AD = 5.76 / 3.2 = 1.8 cm.

Then AB = AD + BD = 3.2 + 1.8 = 5 cm.

Then, by the Pythagorean theorem, CB ^ 2 = AB ^ 2 – AC ^ 2 = 25 – 16 = 9.

СВ = 3 cm.

Answer: Length AB = 5 cm, BC = 3 cm.