In a right-angled triangle ABC (angle C = 90 degrees) AB = 20 cm AC = 16 cm AK bisector. Find ВС, ВK, KС.
| May 7, 2021 | education
In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the leg BC.
BC ^ 2 = AB ^ 2 – AC ^ 2 = 400 – 256 = 144.
BC = 12 cm.
Let the length of the segment KC = X cm, then the length of the ВK = (12 – X) cm.
By the property of the bisector of the angle of a triangle, it divides the side into segments proportional to the adjacent sides.
KC / AC = BK / AB.
X / 16 = (12 – X) / 20.
20 * X = 192 – 16 * X.
36 * X = 192.
X = KC = 192/36 = 49/9 = 5 (4/9) cm.
ВK = 12 – 49/9 = 59/9 = 6 (5/9) cm.
Answer: Leg BC = 12 cm, ВK = 6 (5/9) cm, KС = 5 (4/9) cm.
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