The side edges of a regular quadrangular pyramid are inclined to the base plane at an angle of 60

| September 7, 2021 | education

The side edges of a regular quadrangular pyramid are inclined to the base plane at an angle of 60, the base area is 8.determine 1) the height of the pyramid, 2) the tangent of the dihedral angle at the base of this pyramid

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

Sbn = СD ^ 2 = 8 cm2.

СD = √8 = 2 * √2 cm.

Determine the length of the diagonal of the square ABCD. AC ^ 2 = 2 * AD ^ 2 = 16.

AC = 4 cm.

The diagonals of the square at point O are divided in half, then AO = AC / 2 = 4/2 = 2 cm.

Triangle AOE is rectangular, in which tg60 = OE / AO.

OE = AO * tg60 = 2 * √3 cm.

The side faces of the pyramid are isosceles triangles, then EH, the height, median and bisector of the triangle, then DH = CH, which means the segment OH = AD / 2 = 2 * √2 / 2 = √2 cm, since OH is the middle line of the triangle ACD.

In a right-angled triangle ONE tgOHE = OE / OH = 2 * √3 / √2 = √6.

Answer: The length of the height is 2 * √3 cm, the tangent of the angle is √6.



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