An isosceles triangle, drawn from its vertex, has a length of 6 cm. Find the side if the angle at the vertex is 120 degrees.

The bisector of the ВН of an isosceles triangle, drawn to its base, is also its height and median.

Then AH = CH = AC / 2, and the angle ABН = СВН = ABC / 2 = 120/2 = 600.

In a right-angled triangle ВCH, the angle ВCH = (180 – ВНС – СВН) = (180 – 90 – 60) = 300.

The ВН leg is located opposite an angle of 300, then this leg is half the length of the ВС hypotenuse.

Then BC = 2 * BH = 2 * 6 = 12 cm.

Since ABC is isosceles, then AB = BC = 12 cm.

Answer: The length of the side is 12 cm.