The formula \(d = \sqrt{Hh}\) is derived from the Pythagorean theorem, which states that in a right-angled triangle:
\(a^2 + b^2 = c^2\)
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
In the case of the formula \(d = \sqrt{Hh}\), we are dealing with a right-angled triangle formed by:
- H (the height of the larger triangle)
- h (the height of the smaller triangle)
- d (the distance between the two triangles)
Using the Pythagorean theorem, we can write:
\(H^2 = d^2 + h^2\)
Rearranging the equation to solve for d, we get:
\(d^2 = H^2 - h^2\)
Taking the square root of both sides:
\(d = \sqrt{H^2 - h^2}\)
Simplifying the expression:
\(d = \sqrt{Hh}\)
