The height of a regular triangular pyramid is 16, and the height of its base is 6.

The height of a regular triangular pyramid is 16, and the height of its base is 6. Find the tangent of the angle between the plane of the side face and the plane of the base.

Since the pyramid is regular, at its base lies an equilateral triangle, in which the heights at the point of their intersection are divided in the ratio of 2/1, starting from the top.

OС / OH = 2/1.

OС = 2 * OH.

By condition:

OС + OH = 6 cm.

OС = 6 – OH.

6 – OH = 2 * OH.

OH = 6/3 = 2 cm.

Let us draw the apothem of the DН, and from the right-angled triangle DOН we determine the tangent of the angle DOН, which is the desired angle.

tgDON = DO / OH = 16/2 = 8.

Answer: The tangent of the angle is 8.