In an isosceles triangle, the angle opposite the base is 120 degrees

In an isosceles triangle, the angle opposite the base is 120 degrees, the lateral side is 12 cm. find the height of the triangle drawn to the base.

The height drawn to the base of an isosceles triangle is also the bisector of the angle (halves the angle). This means that the height of the triangle forms two identical right-angled triangles, in which one of the angles is 60 °. If there is an angle of 60 ° in a right-angled triangle, then the leg that forms an angle of 60 ° with the hypotenuse is equal to half of this hypotenuse. That’s why:

h = 0.5 * 12 = 6 cm.

Answer: 6 cm