Trying to use C++ to solve a math problem

[nuzzle]

I had this riddle to solve and I know the answer to be
around ~ 12.31185723778668829963

Note that the precision of a double is only about 17 digits (including all digits before and after the decimal dot). Specifying more digits is superfluous.

Anyway what's that number above and how did you arrive at it?

Looking at the site you referred to you have these relations,

1/h = 1/A + 1/B
A^2 = b^2 - w^2
B^2 = a^2 - w^2

Solved for h you get this formula,

h = 1 / (1/sqrt(b^2 - w^2) + 1/sqrt(a^2 - w^2))

where a and b are the ladder lengths, h is the height above the alley floor up to where the ladders cross, and w is the alley width.

I suppose the number you posted is w, isn't it? When it's entered into the formula,

double a=40.0, b=30.0, w=12.311857237786688;
double h = 1.0 / (1.0/std::sqrt(b*b-w*w) + 1.0/std::sqrt(a*a-w*w));
std::cout << h << std::endl;

the result isn't 10 (as I guess it should be because c=10). So your solution doesn't seem correct.