In triangle ABC, angle B is 60 degrees, side DB is 8. Find side AC.
| September 24, 2021 | education
Since BD is the bisector of the angle ABC, then the angle CBD = ABC / 2 = 60/2 = 30.
In a right-angled triangle CBD, Cos30 = BC / BD.
ВС = ВD * Cos30 = 8 * √3 / 2 = 4 * √3 cm.
In a right-angled triangle ABC tg60 = AC / BC.
AC = BC * tg60 = 4 * √3 * √3 = 4 * 3 = 12 cm.
Answer: The length of the AC leg is 12 cm.
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