The base side and the height of the regular triangular pyramid PTRS are 6 and 8, respectively.

| January 2, 2021 | education

The base side and the height of the regular triangular pyramid PTRS are 6 and 8, respectively. Find the cotangent of the angle between the side edge and the plane of the base of the pyramid.

Since the pyramid is regular, the equilateral triangle TRS lies at its base, and the vertex, point P, is projected into the intersection of the heights, bisectors and medians of the TRS triangle.
Determine the area of the base of the pyramid.
Sbn = TR * TS * Sin60 / 2 = 6 * 6 * Sin60 / 2 = 36 * √3 / 4 = 9 * √3 cm2.
Also Strs = RS * TH / 2.
TH = 2 * Strs / RS = 2 * 9 * √3 / 6 = 3 * √3 cm.
The height TH, at point O, is divided in the ratio 2/1, then AO = 2 * √3 cm, OH = √3 cm.
In a right-angled triangle POT, ctgPTH = TO / PO = 2 * √3 / 8 = √3 / 4.
Answer: The cotangent of the angle between the side edge and the plane of the base is √3 / 4.



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