In a regular triangular pyramid, the side edge is 7 and the side of the base is 10.5 find the height of the pyramid.

The sought height of the pyramid DO is the leg of the right-angled triangle DON. Point O is the center of an equilateral triangle ABC, and point N divides the side of the base BC in half: | CN | = | NB |
You can find the length of this DO leg by knowing the length of the hypotenuse DN and the length of the ON leg.
Point O divides the median АN of the triangle ABC in a ratio of 2: 1. Therefore, | ON | = 1/3 * | AN |
Line segment DN is the median and height of the isosceles triangle BCD and the leg of the triangle BND.