The diagonal of a rectangular parallelepiped with the plane of the base makes an angle of 45 °
| June 28, 2021 | education
The diagonal of a rectangular parallelepiped with the plane of the base makes an angle of 45 °, the sides of the base are 3 and 4 cm. Calculate the height of the parallelepiped.
Let us construct a diagonal BD at the base of the parallelepiped and, by the Pythagorean theorem, determine its length.
BD ^ 2 = AB ^ 2 + AD ^ 2 = 9 + 16 = 25.
ВD = 5 cm.
Diagonal BD is the projection of the diagonal DВ1 onto the plane of the base, then, by condition, the angle ВDВ1 = 45, and the triangle DВВ1 is rectangular and isosceles.
BB1 = BD = 5 cm.
Answer: The height of the parallelepiped is 5 cm.
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