The base of the straight prism ABCDA1B1C1D1 is a rhombus ABCD with angle A equal to 120 degrees and side equal to 4. Find the height of the prism if the angle between the planes ADC1 and ABC is 60 degrees
The segment DC1 is the linear angle of the dihedral angle of the planes ADC1 and ADC, since it is perpendicular to both planes. Then the angle СDС1 = 60.
Since the prism is straight, the CDC1 triangle is rectangular. Then tg60 = CC1 / CD.
√3 = CC1 / 4.
CC1 = 4 * √3 cm.
Answer: The height of the prism is 4 * √3 cm.
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