Equilateral triangle ABC and square BCDE have a common side BC of 4 cm. The plane of the triangle

| January 31, 2021 | education

Equilateral triangle ABC and square BCDE have a common side BC of 4 cm. The plane of the triangle is perpendicular to the plane of the square. Calculate the distance from point A to side DE.

Triangle ABC, by condition, is equilateral. Let’s build the height АН of the triangle ABC, which is also its median. Then the height AH = BC * √3 / 2 = 4 * √3 / 2 = 2 * √3 cm.

Let us draw a segment of the НC perpendicular to the BC, the length of which will be equal to the side of the square. НK = BC = 4 cm.

Since the plane of the square is perpendicular to the plane of the triangle, then AH is perpendicular to the KH, which means that the triangle AНK is rectangular.

НC is the projection of the hypotenuse AK on the plane of the square, then AK is the perpendicular to ED and is the distance from point A to straight line DE.

AK ^ 2 = НK ^ 2 + AH ^ 2 = 16 + 12 = 28.

AK = 2 * √7 cm.

Answer: From point A to DE 2 * √7 cm.



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