In a right-angled triangle ABC, the angle A is 90 degrees, AB = 20 cm; height AD = 12 cm.Find AC and cos C.

univerkov | May 9, 2021 | education

Since AD is the height of a right-angled triangle ABC, then triangles ABD and ACD are rectangular.

Then BD ^ 2 = AB ^ 2 – AD ^ 2 = 400 – 144 = 256.

ВD = 16 cm.

AD ^ 2 = BD * CD.

СD = АD ^ 2 / ВD = 144/16 = 9 cm.

In a right-angled triangle ACD, AC ^ 2 = AD ^ 2 + CD ^ 2 = 144 + 81 = 225.

AC = 15 cm.

CosC = CD / AC = 12/15 = 4/5.

Answer: The length of the AC side is 15 cm, CosC = 4/5.

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