The angle at the apex of an isosceles triangle is 60 degrees, the side is 4.

The angle at the apex of an isosceles triangle is 60 degrees, the side is 4. Find the length of the height drawn to this side

Triangle ABC, by condition, is isosceles, and since the angle at the apex is 60, then triangle ABC is equilateral, since the angles BAC = BCA = 60.

The height of an equilateral triangle, drawn to either side, is also the bisector and median of this triangle.

Then in a right-angled triangle АНC the angle АСН = 60, the angle СН = 30, СН = BН = ВС / 2 = 4/2 = 2 cm.

Then tg60 = AH / CH.

AH = CH * tg60 = 2 * √3 cm.

Answer: The height of the triangle is 2 * √3 cm.