Given a regular triangular pyramid with a side edge of 14, and the side of the base is 9. Find the height of the pyramid.

SABC is a regular triangular pyramid, AB = BC = AC = 9 conventional units, SA = SB = SC = 14 conventional units.
1. The height of a regular pyramid falls to the center of the circle inscribed in the base. Find the radius of the circle inscribed in △ ABC:
CO = a√3 / 3;
CO = 9√3 / 3 = 3√3 (conventional units).
2. Consider △ SOC: SC = 14 conventional units – hypotenuse, ∠SOC = 90 °, СО = 3√3 conventional units and SO – legs. By the Pythagorean theorem, we find the length of SO:
SO = √ (SC² – СО²);
SO = √ (14² – 3√3²) = √ (196 – 9 * 3) = √ (196 – 27) = √169 = 13 (conventional units).
Answer: SO = 13 conventional units.