In an isosceles triangle ABC Base AC = 12, angle ABC = 120. Find a) Height drawn to the rig. b) the side of the triangle.

The height BH of an isosceles triangle ABC is thus its median and bisector of the angle.
Then, AH = CH = AC / 2 = 12/2 = 6 cm, angle ABН = СВН = ABC / 2 = 120/2 = 600.
In a right-angled triangle ВСН tgCBH = СН / ВН.
BH = CH / tg60 = 6 / √3 = 6 * √3 / √3 * √3 = 2 * √3 cm.
By the Pythagorean theorem, we determine the length of the BC hypotenuse.
BC^2 = BH^2 + CH^2 = 12 + 36 = 48.
BC = 4 * √3 cm.
Answer: The length of the BH height is 2 * √3 cm, the length of the side side is 4 * √3 cm.