In a regular triangular pyramid, the sides of the base = 5, and the side edges = 7.

| August 29, 2021 | education

In a regular triangular pyramid, the sides of the base = 5, and the side edges = 7. Find the tangent of the angle between the side edge and the plane of the base.

Triangle ABC, at the base of the pyramid, is equilateral. The medians of the triangle ABC are also its bisectors and heights, point O is the center of the inscribed and circumscribed circle, and the segment WITH is the radius of the circumscribed circle which is equal to: CO = R = AB / √3 = 5 / √3 cm.

In a right-angled triangle COD, according to the Pythagorean theorem, we determine the length of the leg DO.

DO ^ 2 = CD ^ 2 – CO ^ 2 = 49 – 25/3 = 122/3.

DO = 11 / √3 cm.

Then tgOSD = DO / CO = (11 / √3) / (5 / √3) = 11/5 = 2 (1/5).

Answer: The tangent of the angle between the side edge and the plane of the base is 2 (1/5).



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