In a right-angled triangle ABC, angle C = 90 degrees, CD height, AD = 18 cm, DB = 25 cm.Find CD, AC, BC.

univerkov | July 7, 2021 | education

Since the height CD is drawn from the top of the right angle to the hypotenuse, then CD ^ 2 = AD * BD = 18 * 25 = 450.

СD = 15 * √2 cm.

Triangles ACD and BCD are rectangular, then:

AC ^ 2 = CD ^ 2 + AD ^ 2 = 450 + 324 = 774. AC = 3 * √86 cm.

ВС ^ 2 = СD ^ 2 + ВD ^ 2 = 450 + 625 = 1075. ВС = 5 * √43 cm.

Answer: СD = 15 * √2 cm, АС = 3 * √86 cm, ВС = 5 * √43 cm.

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