In a right-angled triangle ABC, angle A = 90 degrees, AB = 20 cm, height AD = 12 cm. find AC and cosC.
| June 20, 2021 | education
From triangle ABD: BD² = AB² – AD² = 400 – 144 = 256 (cm²);
BD = 16 cm;
Triangles ABD and ACD are similar, so AD / BD = DC / AD;
AD² = BD * DC; DC = AD²: BD = 144: 16 = 9 (cm);
BC = BD + DC = 16 + 9 = 25 (cm);
AC² = BC² – AB² = 625 – 400 = 225 (cm²);
AC = 15 s;
cos C = AC / BC = 15/25 = 0.75;
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