In an isosceles triangle ABC, the apex angle is 120 degrees, and the length AB = 2√15 cm

In an isosceles triangle ABC, the apex angle is 120 degrees, and the length AB = 2√15 cm, calculate the length of the median AF.

Consider a triangle ABF, in which the angle B = 120 °, AB = 2√15, BF = √15 are known (AF is the median by condition).
Let us write the cosine theorem for the AF side:
AF² = AB² + BF² + 2 * AB * BF * cos 120 °.
AF² = 60 + 15 + 2 * 2√15 * √15 * (-1/2) = 75 – 30 = 45;
AF = √45 = 3√5 (cm).
Answer: median length AF = 3√5 cm.