From the vertex A of the regular triangle ABC, the perpendicular AM is drawn to its plane.

From the vertex A of the regular triangle ABC, the perpendicular AM is drawn to its plane. Find the distance from point M to the side BC, if AB = 4 cm, AM = 2 cm.

By condition, triangle ABC is correct, therefore AB = BC = AC. Let’s draw the height of AH in triangle ABC, AH in a regular triangle is also the median of the triangle.

Then СН = ВН = ВС / 2 = 4/2 = 2 cm.

Consider a right-angled triangle AСН and, by the Pythagorean theorem, define the leg AН.

AH ^ 2 = AC ^ 2 – CH ^ 2 = 4 ^ 2 – 2 ^ 2 = 16 – 4 = 12.

AH = 2 * √3 cm.

Consider a right-angled triangle MAН, whose angle MAН = 90. We define the hypotenuse MH by the Pythagorean theorem.

MH ^ 2 = AM ^ 2 + AH ^ 2 = 2 ^ 2 + (2 * √3) ^ 2 = 4 + 12 = 16.

MH = √16 = 4 cm.

Answer: The distance from point M to the side of the BC is 4 cm.