Question

Радиус сферы описаной вокруг правильной трехугольной пирамиды 13 см. разстояние от её центра к площади основы пирамиды 5 см. Найти боковое ребро.

Answer 1

думаю 65,но не уверенна.....

Answer 2

Calculation of the lateral edge of a regular triangular pyramid

To find the lateral edge of a regular triangular pyramid, we can use the given information about the radius of the circumscribed sphere and the distance from its center to the base of the pyramid.

Let's denote the radius of the circumscribed sphere as R and the distance from its center to the base of the pyramid as h.

According to the information provided, the radius of the circumscribed sphere is 13 cm, and the distance from its center to the base is 5 cm.

To calculate the lateral edge, we can use the formula:

lateral edge = sqrt(R^2 - h^2)

Substituting the given values, we have:

lateral edge = sqrt(13^2 - 5^2)

Calculating the expression inside the square root:

lateral edge = sqrt(169 - 25)

lateral edge = sqrt(144)

lateral edge = 12 cm

Therefore, the lateral edge of the regular triangular pyramid is 12 cm.

Answer:

The lateral edge of the regular triangular pyramid is 12 cm.