Centroid Of Equilateral Triangle Ratio. Therefore the orthocenter will be exactly two tirds the distance from the angle to the opposite leg of the triangle. Let a be the length of the sides.
To find the height we divide the triangle into two special 30 - 60 - 90 right triangles by drawing a line from one corner to. 23 of height of the equilateral triangle. See bottom set of pictures.
The centroid divides each median into parts in the ratio 21 with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex.
The centroid is the intersection of the three medians. Remember that the centroid divides each median in a ratio of 21. In other words the centroid will always be 23 of the way along any given median. Using this knowledge we can conclude that the orthocenter and the centroid are the same point in an equilateral triangle.
