# Given a rectangular parallelepiped ABCDA1B1C1D1, the base of which is square.

Given a rectangular parallelepiped ABCDA1B1C1D1, the base of which is square. AC = 6√2 cm, AB1 = 4√3 cm. Calculate the degree measure of the dihedral angle В1АDВ.

AC = 6√2 cm, AB1 = 4√3 cm.

∠ В1АD = ∠ В1АВ,

cos B1AB = AB / AB1,

Find AB from triangle ABC. Since ABCD is a square, then:

AB ^ 2 + BC ^ 2 = AC ^ 2,

AB = BC,

AB ^ 2 + AB ^ 2 = AC ^ 2,

2AB ^ 2 = AC ^ 2,

AB ^ 2 = AC ^ 2/2,

AB = √ (AC2 / 2),

AB = √ ((6√2) ^ 2/2),

AB = √ ((36 * 2) / 2),

AB = √ (36),

AB = 6 cm,

cos B1AB = AB / AB1,

cos B1AB = 6: 4√3,

cos B1AB = 3 / 2√3,

cos B1AB = (√3 * √3) / 2√3,

cos B1AB = √3 / 2,

∠ В1АD = ∠ В1АВ = n / 6 = 30 °.

Answer: ∠ В1АD = 30 °.

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