In an isosceles triangle AB = BC = 2 cm, AC = 1. Find the length of the median AM. How do I find her?

Let’s draw the height BH of the isosceles triangle ABC, which will also be its median, then CH = AC / 2 = 1/2 cm.

Determine the cosine of the angle BCH in the right-angled triangle BCH.

CosВСН = СН / ВС = (1/2) / 2 = 1/4 = 0.25.

Since AM is the median, then CM = BM = BC / 2 = 2/2 = 1 cm.

In the triangle AMC, we apply the cosine theorem and determine the length of the median AM.

AM ^ 2 = AC ^ 2 + CB ^ 2 – 2 * AC * CM * CosBCH = 1 + 1 – 2 * 1 * 1 * 0.25 = 2 – 0.5 = 1.5.

AM = √1.5 cm.

Answer: The length of the median is √1.5 cm.