In a rectangular parallelepiped, the side edge is 5 cm, the area of the diagonal section is 25 roots from 3 cm2.

In a rectangular parallelepiped, the side edge is 5 cm, the area of the diagonal section is 25 roots from 3 cm2. Calculate the angle between the diagonal of the box and the plane of the bottom base.

The diagonal section of a parallelepiped is a rectangle АА1С1С.

Knowing the cross-sectional area and the length of one of its measurements, we determine the length of the side of the AC section.

Ssech = АА1 * АС.

AC = Ssection / AA1 = 25 * √3 / 5 = 5 * √3 cm.

The angle between the A1C diagonal and the base plane is the ACA1 linear angle.

From the right-angled triangle АА1С we determine the tangent of the angle АСА1.

tgACA1 = AA1 / AC = 5/5 * √3 = √3 / 3.

tgACA1 = arctan (√3 / 3) = 30.

Answer: The angle between the diagonal and the base plane is 30.



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