From the center O of the regular triangle ABC, a perpendicular OM is drawn to the plane ABC

| May 25, 2021 | education

From the center O of the regular triangle ABC, a perpendicular OM is drawn to the plane ABC with a length of 2 cm. Calculate the distance from point M to the side of the triangle ABC if AB = 4cm.

The center of a triangle is the point of intersection of its medians. Since triangle ABC is, by condition, regular, its medians are also the heights and bisectors of the triangle.

The height of an equilateral triangle is equal to: CH = AB * √3 / 2 = 4 * √3 / 2 = 2 * √3 cm.

The point of intersection of the medians divides it in a ratio of 2/1, starting from the top, then OH = CH / 3 = 2 * √3 / 3 cm.

The distance from point M to the sides of the triangle is the height of the side face of the triangle.

In a right-angled triangle MOН, according to the Pythagorean theorem, MH ^ 2 = OH ^ 2 + OM ^ 2 = (12/9) + 4 = 48/9.

MH = 4 * √3 / 3 cm.

Answer: From point M to the sides of the triangle 4 * √3 / 3 cm.



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