I've been staring at the first problem from May '98. I understand the solution, but I still don't understand how it's possible.
It's because theta is so small. Considering a right triangle of height h and a much longer base, h must be quite large for the hypotenuse to be 6 m longer than the base. Below is a simple example:
base 1000
hypotenuse 1006
height 109.7087052
Right triangle here is of course an approximation to the original problem, just to demonstrate what is going on.