In a rectangular triangle ABC, CK is the height from the right angle to the hypotenuse.
| July 11, 2021 | education
In a rectangular triangle ABC, CK is the height from the right angle to the hypotenuse. Leg BC = 20 cm. KB-AK = 7cm, KB: AK = 16: 9 Find AC = x.
By condition:
KB – AK = 7. (1)
KB / AK = 16/9 (2).
Let us solve the system of two equations by the substitution method
KB = 7 + AK.
(7 + AK) / AK = 16/9.
16 * AK = 63 + 9 * AK.
7 * AK = 63.
AK = 63/7 = 9 cm.
KB = 7 + 9 = 16 cm, then AB = 9 + 16 = 25 cm.
By the Pythagorean theorem, AC ^ 2 = AB ^ 2 – BC ^ 2 = 625 – 400 = 225.
AC = 15 cm.
Answer: The length of the AC leg is 15 cm.
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