ABCDA1B1C1D1-cubic meter find the angle between the plane passing through points B, D

| August 7, 2021 | education

ABCDA1B1C1D1-cubic meter find the angle between the plane passing through points B, D and C1 and the plane of the base.

Let the length of the edge of the cube be X cm.

Determine the length of the AC diagonal at the base of the cube.

The ACD triangle is rectangular, then AC ^ 2 = AD ^ 2 + CD ^ 2 = X ^ 2 + X ^ 2 = 2 * X ^ 2.

AC = X * √2 cm.

The diagonals of the square ABCD intersect at right angles and are halved at point O.

Then OC = X * √2 / 2 cm.

Section BC1D is an isosceles triangle, then OC1 is its height, OC is the projection of the inclined OC1 onto the base plane, then the linear angle COC1 is the desired angle. In a right-angled triangle OCC1, tgCOC1 = CC1 / OC = X / (X * √2) / 2 = 2 / √2 = √2. SOC1 angle = arctg√2.

Answer: The angle between the planes is arctg√2.



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