# The base of the straight prism ABCDA1B1C1D1 is a rhombus ABCD with angle A equal to

September 21, 2021 | education

| **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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