We would apply the theorem which states that the sum of the distances from an arbitrary point inside an equilateral triangle to the sides of the triangle is equal to the altitude of the triangle.
Given that the length of each side of the traingle is 8 in, the length of the altitude would be determined by applying pythagoras theorem. The diagram is attached below
The altitude is represented by h
From pythagoras theorem,
Hypotenuse^2 = opposite side^2 + adjacent side^2
8^2 = h^2 + 4^2
64 = h^2 + 16
h^2 = 64 - 16 = 48
h = square root of 48
h = 6.9 inches
the sum of the distances from a point A inside the triangle to the sides of the triangle is 6.9 inches