ABCDA1B1C1D1 – rectangular parallelepiped, with BC = 3a, CD = a, CC1 = 6a.
| August 13, 2021 | education
ABCDA1B1C1D1 – rectangular parallelepiped, with BC = 3a, CD = a, CC1 = 6a. Find the tangent of the angle between the planes BCD1 and ABC.
Since, by condition, the parallelepiped is rectangular, all of its faces are rectangles.
The DD1C1C face is a rectangle. The opposite sides of the rectangle are equal, DD1 = CC1 = 6 * a.
The tangent of the angle between the planes BCD1A1 and ABCD is equal to the tangent of the angle between the ribs CD and CD and is equal to the ratio of the opposite leg to the adjacent one.
tgDСD1 = DD1 / СD = 6 * a / a = 6.
Answer: The tangent of the angle between the planes is 6.
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