Question

The sides of an equilateral triangle measure 6cm each. Find the distance between the plane of the triangle and a point P which is 13cm from each vertex of the triangle. I need an illustration.

Answer 1

Imagine the equilateral triangle on a piece of paper, and there's a point which is 13 cm from each vertex of the triangle in mid air. Now find the distance between the paper and that point

Answer 2

So what't the solution?

Answer 3

well assuming what I said earlier is even correct, the distance between the center of an equilateral triangle and a vertex is \[\frac{ L }{ \sqrt{3} }\] so the answer will be
\[ans = \sqrt{13^{2} - ({\frac{ L }{\sqrt{3} }}})^{2} \] as L = 6 cm
ans = 12.52 cm