BE perpendicular to the plane of the square ABCD. Find the distance from point E to straight

| August 22, 2021 | education

BE perpendicular to the plane of the square ABCD. Find the distance from point E to straight lines BC, CD, AC, if BC modulo = 3cm, CE modulus = 4cm.

The distance from point E to line CD is a segment EC, since BC is perpendicular to CD, as the sides of a square, and BC is a projection of EC, then EC is perpendicular to CD.

EC = 4 cm.

The distance from E to line BC is the segment BE itself, since it is perpendicular to the plane of the square. BE ^ 2 = EC ^ 2 – BC ^ 2 = 16 – 9 = 7. BE = √7 cm.

Let’s draw a diagonal AC of the square, the length of which will be equal to: AC ^ 2 = AB ^ 2 + BC ^ 2 = 9 + 9 = 18.

AC = 3 * √2 cm. Since ABCD is a square, its diagonals are equal, intersect at right angles and are halved. Then ВН = AC / 2 = 3 * √2 / 2.

Then from the triangle ВEН, EH ^ 2 = EB ^ 2 + BH ^ 2 = 7 + 18/4 = 7 + 4.5 = 11.5.

EH = 3.4 cm.

Answer: Distance EB = √7 cm, EC = 4 cm, EH = 3.4 cm.



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