Question

(5p) 6. Se consideră o piramidă triunghiulară regulată VABC, de vârf V şi bază ABC. Dacă AB = 6 cm şi VA = 2√6 cm, atunci: a) Determinați distanţa de la punctul A la planul (VBC).​

Answer 1

first need to find the height of the pyramid, h. We can use the Pythagorean theorem to find the height of the pyramid, as follows:VA^2 = h^2 + (AB/2)^2

(2√6)^2 = h^2 + (6/2)^2

12 = h^2 + 9

h^2 = 3

h = √3Next, we can use the height and the distance from point A to the plane (VBC) to form a right triangle. Let's call this distance d.d^2 + h^2 = VA^2

d^2 + 3 = 12

d^2 = 9

d = 3So the distance from point A to the plane (VBC) is 3 cm.