In a right-angled triangle ABC C = 90, CD – height, AD = 18 cm, DB = 25 cm.Find CD, AC, BC.
| May 26, 2021 | education
Since the height CD is drawn from the top of the right angle to the hypotenuse, then CD ^ 2 = BD * AD = 25 * 18 = 45.
СD = 15 * √2 cm.
From the right-angled triangle ACD, we determine the length of the hypotenuse AC.
AC ^ 2 = CD ^ 2 + AD ^ 2 = (15 * √2) ^ 2 + 18 ^ 2 = 450 + 324 = 774.
AC = 3 * √86 cm.
In a right-angled triangle ABC, we determine the length of the BC leg.
BC ^ 2 = AB ^ 2 – AC ^ 2 = 1849 – 774 = 1075.
BC = 5 * √43 cm.
Answer: The length of the segment CD = 15 * √2 cm, AC = 3 * √86 cm, BC = 5 * √43 cm.
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