In a right-angled triangle ABC, the height CD is drawn to the hypotenuse AB. Find the leg length AC if AB = 9 cm, BD = 4 cm.
| August 8, 2021 | education
Determine the length of the segment AD.
AD = AB – BD = 9 – 4 = 5 cm.
Since CD is the height drawn from a right angle to the hypotenuse, the square of its length is equal to the product of the lengths of the segments by which the height divides the hypotenuse.
CD ^ 2 = AD * BD = 5 * 4 = 20.
The ACD triangle is rectangular, then, by the Pythagorean theorem, we determine the length of the AC side.
AC ^ 2 = CD ^ 2 + AD ^ 2 = 20 + 25 = 45.
AC = √45 = 3 * √5 cm.
Answer: The length of the AC leg is 3 * √5 cm.
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