I completing complex math via correspondence .. don't have a teacher to refer to, so if you could check me equation/answer and advise would be much appreciated.
Anyway, here is how I would do it:
First, I suggest finding the height of the "roof" (that is, the length of the perpendicular between and ). Call it , and we have:
Now everything follows from the Pythagorean theorem:
is found in much the same way, and since the two inner right triangles are congruent (two sides and an included angle equal).
Now, I wouldn't expect you to "see" how I made that jump because I skipped a bunch of steps in-between. But the idea was that you could get to the same answer if you used the same starting point. Here is what I did:
(Taking square root of both sides; we can ignore the negative root since )
(Splitting square root: )
And of course, if you are just looking for an approximation, you could have stopped at the first step and threw it into the calculator. I just like keeping things in their exact value.
From Reckoner's last post, he found the altitude h.
One side of the right triangle is already known to be 10000, and now we can find the hypotenuse "a" using the Pathagorean theorem.
Substituting for h, we have: