Solid geometry › Polyhedra and sections › Angles in pyramids

Side length of a square tilted to a plane

High school · ●●●●○ 100 pts

Given a square ABCDABCD with side length aa, vertex AA lies in plane β\beta, and the other vertices are on the same side of plane β\beta. The distances from points BB and DD to plane β\beta are 1 and 2, respectively. If the angle between plane ABCDABCD and plane β\beta is 30∘30^\circ, find aa. Round to two decimal places.

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dihedral angletriangle arealaw of cosines