Given a rectangular parallelepiped ABCDA1B1C1D1, the base of which is square.
| January 31, 2021 | education
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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