The side of a regular triangle ABC = 2√3, a perpendicular AK = 4cm is drawn to the plane of triangle

The side of a regular triangle ABC = 2√3, a perpendicular AK = 4cm is drawn to the plane of triangle ABC. Find out the distance from AK to BC

Let’s build the height АН of the equilateral triangle ABC.

In an equilateral triangle, all interior angles are 60. In a right-angled triangle ABH, Sin60 = AH / AB.

AH = AB * Sin60 = 2 * √3 * √3 / 2 = 3 cm.

AH is the projection of the inclined KH, and since AH is perpendicular to BC, then KH is perpendicular to BC, then KH is our desired distance.

Since AK is perpendicular to the plane of the triangle, then the triangle AKH is rectangular, in which, according to the Pythagorean theorem, KH ^ 2 = AK ^ 2 + AH ^ 2 = 16 + 9 = 25.

KH = 5 cm.

Answer: From point K to the BC side 5 cm.