The height of a regular triangular pyramid is 8 m. The angle between the planes of the side face

| April 28, 2021 | education

The height of a regular triangular pyramid is 8 m. The angle between the planes of the side face and the base is 30. Calculate the length of the apothem of the pyramid.

Since the pyramid is regular, an equilateral triangle lies at its base, and its side faces are isosceles triangles.

Since the angles between the side faces are equal, the top of the pyramid is projected to point O, the point of intersection of the heights and medians of the equilateral triangle ABC.

Let us construct apothem DH, which is the height and median of the BCD face.

Then the triangle DOH is rectangular, in which, by condition, the angle BHO = 30.

The DO leg lies opposite the angle 30, then the length of the hypotenuse DH is equal to two lengths of the DO leg.

DН = 2 * DO = 2 * 8 = 16 m.

Answer: Dina of apothem is 16 m.



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