In a rectangular parallelepiped, the measurements are 4 cm, 8 cm 4 roots of 5.

| February 25, 2021 | education

In a rectangular parallelepiped, the measurements are 4 cm, 8 cm 4 roots of 5. Find the angle between the diagonal of the parallelepiped and the plane of its base.

The length of the diagonal is determined through the lengths of the sides of the parallelepiped.

The square of the length of the diagonal of a parallelepiped is equal to the sum of the squares of the lengths of its sides.

AC1 ^ 2 = AA1 ^ 2 + AD ^ 2 + CD ^ 2 = 80 + 64 + 16 = 160.

AC1 = 4 * √10cm.

Let’s draw a diagonal AC at the base of the parallelepiped. If the height of the parallelepiped is 4 * √5 cm, then in a right-angled triangle ACC1

SinCAC1 = CC1 / AC1 = 4 * √5 / 4 * √10 = √5 / √5 * √2 = 1 / √2 = √2 / 2. Angle CAC1 = Arcsin (√2 / 2) = 45.

Answer: The angle between the diagonal and the base is 45.



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