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

**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).