Angle B of an isosceles triangle ABC is 120 degrees. Find the distance from the top of C to line AB, if AC = 30cm.

In an isosceles triangle, the angles at the base are equal. Since there cannot be two angles of 120 ° in a triangle (since the sum of the angles in any triangle is 180 °), then 120 ° = angle B is the apex of an isosceles triangle. Find angles A and C:

∠А = ∠С = (180 ° – 120 °) / 2 = 60 ° / 2 = 30 °.

Let’s draw the height of the CК from point C to line AB (it can be located both in the triangle ABC and outside of it). We get a right-angled triangle AKС, in which ∠А = 30 °, ∠ К = 90 °. In a right-angled triangle with an angle of 30 °, the leg opposite to the angle of 30 ° is half the hypotenuse. Therefore, КC = 1/2 * AC = 1/2 * 30 cm = 15 cm.