Since FriendRob specified “You want to make it as tall as possible”, I think that ouryL is thinking of building the shelves the smart way, which is in situ. I’ve built floor-to-ceiling bookshelves several times, and either done it directly agains the wall (i.e. no back), or a couple of feet away from the wall, nailed the back on, and walked the resulting structure toward the wall. Bingo! Half an inch of clearance floor-to-ceiling is ample.
Or aren’t we allowed to think outside the box?
[[nitpick]
Even if you’re building the bookshelf on the floor and raising it, you don’t need sines, cosines, etc. Just c = sqrt (a^2 + b^2), so it’s not really an example of the OP.
[/nitpick]
Sine and cosine can be used to solve the bookshelf problem, but as in Perl, there’s more than one way to do it.
[spoiler]We assume that you can rotate the base of the shelves to be parallel to the desired wall inside the room for which you’re building the shelves, and that you’re performing the last assembly inside that room. The hypotenuse of the shelf’s sides has to be no more than 8 feet or 96 inches. The shelf depth has to be at least 9" to fit your math textbooks, comic books, and other large format hardbacks. Knowing that, you can say that
9[sup]2[/sup] + x[sup]2[/sup] = 96[sup]2[/sup]
x[sup]2[/sup] = 96[sup]2[/sup] - 9[sup]2[/sup]
x[sup]2[/sup] = 9216 - 81 = 9135
x = SQRT(9135) = approx. 95.57"
Carpenter’s Answer: leave a half-inch off the top if you’ve got hardwood floors; otherwise leave off an inch just to be safe.[/spoiler]
Aargh! I meant “Half an inch of clearance between the top of the bookcase and the ceiling is ample” (because the bookcase sides are raised before being attached to the shelves).
Without wanting to un-spoiler Jurph, I’d have said that three centimeteres would have been more than enough space.
And who the hell needs a bookcase to fit that snugly, without simply fitting it to the walls? I suspect a mathematician is in our midsts…
Meaning that is the everyday relevance I get out of mathematics. I am learning how to deal with stuff I dislike and don’t understand and still keep my sanity.
Just for the hell of it, I figured out the exact max height of a bookshelf with shelves 25 cm deep that can be rotated up with ceilings of a height of 2 m. It’s about 1.98 meters, which in a room with 8 ft ceilings, would actually be about 7’11.25". So I was mistaken earlier.
YES! We are to determine the height of the shelves.
Suppose the shelves are only 1" deep (for very small books) as opposed to say a nominal 9" deep shelves to accomodate most books. This affects the answer.
For 9" shelves H = 95.56." Make the reaar of the shelves 95.5" and the front or front valence 95.9" for a mimimum gap.