The diagonal of a regular quadrangular prism is inclined to the plane of the base

univerkov | September 5, 2021 | education

The diagonal of a regular quadrangular prism is inclined to the plane of the base at an angle of 60. The side of the base is equal to 3 root of 6. Find the side edge.

Since the prism is correct, there is a square at its base.

The diagonal AC divides the square ABCD into two right-angled isosceles triangles. Angle CAD = ACD = 45.

Then AC = AD / SinACD = 3 * √6 / (√2 / 2) = 6 * √3 cm.

Triangle АА1С is rectangular, then tgАСА1 = АА1 / АС.

АА1 = АС * tg60 = 6 * √3 * √3 = 18 cm.

Answer: The length of the side rib is 18 cm.

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