In the right-angled triangle ABC, the height CD is drawn to the hypotenuse AB.
| June 12, 2021 | education
In the right-angled triangle ABC, the height CD is drawn to the hypotenuse AB. Find the length of the AC leg if AB = 9 cm, BD = 5 cm.
Determine the length of the segment AD. AD = AB – BD = 9 – 5 = 4 cm.
CD is the height of a right-angled triangle, drawn to the hypotenuse, then CD2 = AD * BD = 5 * 4 = 20.
In a right-angled triangle ACD, by the Pythagorean theorem, we define AC.
AC ^ 2 = AD ^ 2 + CD ^ 2 = 16 + 20 = 36. AC = 6 cm.
Answer: The length of the AC leg is 6 cm.
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