An equilateral triangle lies at the base of the KABC pyramid. Side edge KB perpendicular

| September 23, 2021 | education

An equilateral triangle lies at the base of the KABC pyramid. Side edge KB perpendicular to the plane of the triangle. Find the side of the base of the pyramid if the dihedral angle at the AC edge is 30 degrees and KB = 2 cm.

Let’s build the height BH of an equilateral triangle ABC.

From point K we construct a segment KН. Since, by condition, BK is perpendicular to the base of the pyramid, BH is the projection of the inclined BH onto the ABC plane. Then the linear angle BНK = 30, since there is a dihedral angle at the edge AC.

In a right-angled triangle BKН, tg30 = BK / BН. BH = BK / tg30 = 2 / (1 / √3) = 2 * √3 cm.

The segment BH is the height of an equilateral triangle. BH = AC * √3 / 2.

AC = 2 * BH / √3 = 2 * 2 * √3 / √3 = 4 cm.

Answer: The length of the side of the base of the pyramid is 4 cm.



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