Since the segment AD is height, the triangles ADB and ACD are rectangular.
In a right-angled triangle ABD CosBAD = AD / AB = 12/20 = 3/5.
Right-angled triangles ABD and ACD are similar in acute angle, then CosACD = CosBAD = 3/5.
Determine the sine of the angle ACD.
Sin2АСD = 1 – Cos2АСD = 1 – 9/25 = (25 – 9) / 25 = 16/25.
SinАСD = 4/5.
SinАСD = АD / АС = 4/5.
AC = 5 * AD / 4 = 5 * 12/4 = 15 cm.
Answer: The length of the AC leg is 15 cm, CosC = 3/5.
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