A regular triangular pyramid is given. the height of the pyramid is equal to the side
| January 31, 2021 | education
A regular triangular pyramid is given. the height of the pyramid is equal to the side of the base and is equal to 32 cm. Find the angle between the side edge and the base of the pyramid.
Since the pyramid is regular, the equilateral triangle ABC lies at its base.
Height D is projected to point O, the point of intersection of medians, bisectors and heights.
AH = BC * √3 / 2 = 16 * √3 cm.
Point O divides the segment AH in a ratio of 2/1.
AO = 2 * OH.
AO = AН * 2/3 = 16 * √3 * 2/3 = 32 * √3 / 3 cm.
In a right-angled triangle, AOD tgOAD = OD / AO = 32 / (32 * √3 / 3) = 3 / √3 = √3.
OAD angle = 600.
Answer: The angle between the side edge and the base is 600.
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