The height of the base of a regular triangular pyramid is 8 cm, and the dihedral angle at the side

| February 1, 2021 | education

The height of the base of a regular triangular pyramid is 8 cm, and the dihedral angle at the side of the base is 60 degrees. Find the side edge of the pyramid.

The height AH of an equilateral triangle ABC is also its median, which at point O is divided in the ratio 2 / 1. Then the length of the segment OH = 8/3 cm.

The DOН triangle is rectangular, then tg60 = OD / OH.

OD = OH * tg60 = (8/3) * √3 = 8 * √3 / 3 cm.

The length of the segment AO = AH – OH = 8 – 8/3 = (24 – 8) / 3 = 16/3 cm.

In a right-angled triangle ADO, according to the Pythagorean theorem, we determine the length of the hypotenuse of AD.

AD ^ 2 = AO ^ 2 + DO ^ 2 = (16/3) ^ 2 + (8 * √3 / 3) ^ 2 = 256/9 + 192/9 = 448/9.

AD = 8 * √7 / 3 cm.

Answer: The length of the side rib is 8 * √7 / 3 cm.



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