In triangle ABC it is known that C = 90 °, tgB = 5 and AB = 26 cm.Find 12 the length of the smaller leg of the triangle.

univerkov | December 3, 2020 | education

TgB = AC / CB = 5/12
AC = CB • 5/12
AB² = AC² + BC² = 25/144 * CB² + CB² =
(25 + 144) / 144 * CB² = 26²
(13/12) ² * CB² = 26²
13/12 * CB = 26
CB = 26 * 12/13 = 2 * 12 = 24
AC = CB * 5/12 = 24 * 5/12 == 10
answer 10 cm

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