An equilateral triangle is a triangle in which all sides are the same size, and the angles are 60 degrees. The median in such a triangle is a segment that connects any of its vertices and the middle of the opposite side. In an equilateral triangle, the median will also be the bisector and the height.
Let two medians AO and SK be drawn in the triangle ABC. Then we need to find the value of the angle AMK in the right-angled triangle AKM (angle AKM – straight line), taking into account that AKM + KAM + AMK = 180 °.
Let’s find the value of the angle KAM in the triangle AKM:
60: 2 = 30 °.
Let’s find the value of the angle AMK:
180 – 90 – 30 = 60 °.
Answer: The acute angle between the two medians will be 60 °.
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