Triangle AB = 4 BC = 6 angle ABC = 60 find the height BD.

By the cosine theorem, we define the length of the AC side.

AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Сos60 = 16 + 36 – 2 * 4 * 6 * 1/2 = 52 – 24 = 28.

AC = √28 = 2 * √7 cm.

Let’s define the area of the triangle ABC in two ways.

Savs = (1/2) * AB * BC * Sin60 = (1/2) * 4 * 6 * √3 / 2 = 6 * √3 cm2.

Sаvs = АС * ВН / 2 = ВН * 2 * √7 / 2 = = ВН * √7 cm2.

BH * √7 = 6 * √3.

BH = 6 * √3 / √7 = 6 * √21 / 7 cm2.

Answer: The height of the triangle is 6 * √21 / 7 cm2.