The base of the right parallelepiped ABCD A1B1C1D1 is the parallelogram ABCD, in which AB = √2cm
| September 20, 2021 | education
The base of the right parallelepiped ABCD A1B1C1D1 is the parallelogram ABCD, in which AB = √2cm, AD = 1cm, angle BAD = 45 degrees. calculate the length of the side edge of the parallelepiped if the degree measure of the angle of inclination of its smaller diagonal to the plane of the base is 30 degrees
In triangle ABD, to determine the length BD, we use the cosine theorem for a triangle.
BD² = AB² + AD² – 2 * AB * AD * Cos45 = (√2) 2 + 12 – 2 * √2 * 1 * √2 / 2 = 3 + 1 = 4.
ВD = 2 cm.
In a right-angled triangle B1BD, the angle B1DB = 30, then the length of the leg BB1 = DB * tg30 = 2 * 1 / √3 = 2 / √3 cm.
Answer: The length of the side rib is 2 / √3 cm.
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